Magyar változat/Hungarian version

The English and the Hungarian versions differ significantly.

Personal data

Tóth, János CV
Ph D (candidate of the mathematical science)
Department of Mathematical Analysis
Institute of Mathematics
Faculty of Sciences
Budapest University of Technology and Economics
Budapest, Műegyetem rkp. 3-9.
P. O. Box 91, H-1521 HUNGARY
Tel.: (36-1)463-2314 or (36-1)463-2475
Home: (36-1)242-06-40
Fax: (36-1)463-3172
E-mail: jtoth@math.bme.hu
Home: jtoth@helka.iif.hu

Topics for PhD theses

Qualitative and quantitative investigations of polynomial models with special reference to applications in reaction kinetics, population biology, biochemistry etc.

Applications and comparisons of mathematical program packages (such as Mathematica and Maple V) in one of the areas of applied calculus

Scientific activity

Selected publications

Books

Csermely, P., Gergely, P., Koltay, T., Tóth, J.: Research and Publication in Science, Osiris, Budapest, 1999 (in Hungarian).

Preface
1. Science and research: Basic notions. Methods of cognition. What are good scientists like? Where to do research? What to research? Experiments. Evaluation. Models. Ethical and sociological questions.
2. Literature and the libraries: Use and structure of the literature. The process of collecting literature.
3. Informal communication: Communication inside the laboratory and between laboratories. Electronic communication.
4. Formal communication: Publications. Scientific results in the media. The role of media. Conferences. How to write papers in English?
5. Proposals and projects: the financial background of research.
References (7 pages).
The most important reference books and other documents (including web sites) of individual areas of science: Science and engineering in general. Agricultural Sciences. Engineering Science. (37 pages)
*(8 independent citations)*
Research and Publication in Science

Mathematical Models of Chemical Reactions Érdi, P., Tóth, J.: Mathematical Models of Chemical Reactions. Theory and Applications of Deterministic and Stochastic Models, Manchester University Press, Manchester, Princeton University Press, Princeton, 1989.

1. Chemical kinetics: a prototype of nonlinear science.
2. The structure of kinetic models: Temporal processes. Properties of process-time. Structure of the state-space. Nature of determination.
3. Stoichiometry: the algebraic structure of complex chemical reactions.
4. Mass action kinetics deterministic models: Exotic reactions. Multistationarity. Oscillatory reactions. Chaotic phenomena. Inverse problems. Lumping.
5. Continuous time discrete state stochastic models: Internal fluctuations. Fluctuation-dissipation theorem. Enzyme kinetics. Stationary distributions. External fluctuations.
6. Chemical reactions accompanied by diffusion.
7. Applications: Biochemistry. Neurochemistry. Lotka-Volterra models. Ecology. Chemical circuits. Selection.
References (32 pages).
Index.
*(140 independent citations)*

Szili, L., Tóth, J.: Mathematics and Mathematica, ELTE Eötvös Kiadó, Budapest, 1996.

1. Mathematical program packages: Symbolic packages (CAS: computer algebra systems). Numerical packages.
2. Mathematica fundamentals: Basic principles. External connexions. Sources of information.
3. Chapters of mathematics: Fundamentals. Expressions. Equations. Calculus. Differential equations. Discrete mathematics. Geometry. Linear algebra. Number theory. Probability theory. Mathematical statistics.
4. Programming Mathematica: Elements. How to make programs faster? Advice to programming. Writing your own packages.
5. Applications outside mathematics: Bussiness graphics. Sound. Time. Physics. Geography. Chemistry.
References (90 items).
Index.
Mathematics and Mathematica

 
Differential equations Tóth, J.; Simon, P.: Differential equations. Introduction into the theory and its applications, TYPOTEX, Budapest, 2005 (In Hungarian).
Preface
I. Fundamentals
1. Introduction, notations.
2. Basic notions, motivation. Elementary qualitative and quantitative methods. Existence and uniqueness results.
3. Solution methods for classes of equations of simple form
II. Linear equations
4. First order linear differential equations
5. Higher order equations
6. The Laplace transform
III. Elements of the qualitative theory
7. Elements of stability theory
8. Autonomous equations, dynamical systems
IV. Addenda
9. Partial differential equations
10. Elements of the calculus of variations
11. Solution of the problems
References (??? items).
Index.

 

Papers

  • Arányi, P.; Tóth, J.: A full stochastic description of the Michaelis-Menten reaction for small systems, Acta Biochimica et Biophysica Academiae Scientificarum Hungariae 12 (4) (1977), 375-388. zipped gifs.
    The Kolmogorov-equations for the stochastic model of the Michaelis-Menten reaction is explicitly solved by a method in the special case when the number of enzyme molecules is exactly one, which can also be extended for cases with a few enzyme molecules. The important differences between the stochastic and deterministic approaches and their biological significance is analyzed. Beside the symbolic solution of the time course of the irreversible reaction the equilibrium is also described for the reversible case. Comparisons are made with the usual steady state approximation.
    *(16 independent citations)*
  • Blickle, T.; Halász, G.; Tóth, J.: Structures, hypergraphs and knowledge representation in chemical engineering science. I - Problem formulation, The International Journal for Artificial Intelligence in Engineering 5 (3) (1990), 142-152. *(1 independent citation)*
  • Brochot, C., Tóth, J.; Bois, F.: Lumping in pharmacokinetics, Journal of Pharmacokinetics and Pharmacodynamics, 32 (5-6) (2005), 719-736. online. manuscript here.
    Pharmacokinetic models simplify biological complexity by dividing the body into interconnected compartments. The time course of the chemical's amount in each compartment is then expressed as the solution to a system of ordinary differential equations. Difficulties arise when the model contains more variables and parameters than comfortable for mathematical and computational treatment. To overcome such difficulties the new and powerful tools of lumping are applied, which are aimed at reducing a differential system by aggregating several variables into one. The lumped model is a differential equation system, whose variables are interpretable in terms of variables of the original system. The reduced model is usually required to satisfy some constraints: it may be necessary to keep state variables of interest for prediction unlumped. For this purpose constrained lumping methods have are also available. After presenting the theory, we study, here, through practical examples, the potential of such methods in toxico/pharmacokinetics. We first simplify a 2-compartment pharmacokinetic model by symbolic lumping. We then explore the reduction of a 6-compartment physiologically based pharmacokinetic model for 1,3-butadiene with numerical constrained lumping.
    *(5 independent citations)*
  • Császár, A.; Érdi, P.; Jicsinszky, L.; Tóth, J.; Turányi, T.: Several exact results on deterministic exotic kinetics, Zeitschrift für Physikalische Chemie, (Leipzig) 264 (1983), 449-463. *(3 independent citations)*
  • Csikja, R.; Tóth, J.: Blow up in polynomial differential equations, Enformatika. International Journal of Applied Mathematics and Computer Sciences 4 (2) (2007), 728-733. manuscript here.
  • Egri, E.; Tóth, J.; Brochot, C.; Bois, F.: Symbolic lumping of some catenary, mamillary and circular compartmental systems (in preparation).
  • Eső, P.; Simonovits, A.; Tóth, J.: Designing benefit rules for flexible retirement: Welfare vs. redistribution (submitted)
  • Érdi, P.; Kiss, T.; Tóth, J.; Ujfalussy, B.; Zalányi, L.: From systems biology to dynamical neuropharmacology: proposal for a new methodology, Systems Biology, IEEE Proc. 153 (4) (2006), 299-308.
    The concepts and methods of systems biology are extended to neuropharmacology in order to test and design drugs for the treatment of neurological and psychiatric disorders. Computational modelling by integrating compartmental neural modelling techniques and detailed kinetic descriptions of pharmacological modulation of transmitter-receptor interaction is offered as a method to test the electrophysiological and behavioural effects of putative drugs. Even more, an inverse method is suggested as a method for controlling a neural system to realise a prescribed temporal pattern. In particular, as an application of the proposed new methodology, a computational platform is offered to analyse the generation and pharmacological modulation of theta rhythm related to anxiety.
    Archived manuscript. *(4 independent citations)*
  • Érdi, P.; Tóth, J.: Stochastic reaction kinetics: "Nonequilibrium thermodynamics" of the state space?, Reaction Kinetics and Catalysis Letters 4 (1) (1976), 81-85. manuscript *(1 independent citation)*
  • Érdi, P.; Tóth, J.: Some comments on Prigogine's theories, Reaction Kinetics and Catalysis Letters 11 (4) (1979), 371-375. manuscript *(1 independent citation)*
  • Érdi, P., Tóth, J.: What is and what is not stated by the May-Wigner theorem?, J. Theor. Biol. 145 (1990), 137-140. *(7 independent citations)*
  • Frankowicz, M., Moreau, M., Szczesny, P. P., Tóth, J., Vicente, L.: Fast variables elimination in stochastic kinetics, J. Phys. Chem. 97(1993), 1891-1895. manuscript *(7 independent citations)*
  • Gaveau, B.; Martinás, K.; Moreau, M.; Tóth, J.: Entropy, extropy and information potential in stochastic systems far from equilibrium, Physica A (Statistical Mechanics and its Applications) 305A (3-4) (2002), 445-466. manuscript *(6 independent citations)*
  • Gaveau, B., Moreau, M., Tóth, J.: Decay of the metastable state: different predictions between discrete and continuous models, Letters in Mathematical Physics 37 (1996), 285-292. *(4 independent citations)*
  • Gaveau, B.; Moreau, M.; Tóth, J.: Master equation and Fokker-Planck equation: Comparison of entropy and rate constants, Letters in Mathematical Physics 40 (1997), 101-115. *(2 independent citations)*
  • Gaveau, B.; Moreau, M.; Tóth, J.: Dissipation of energy and information in nonequilibrium reaction-diffusion systems, Physical Review E 58 (11) (1998), 5351-5354. manuscript. *(6 independent citations)*
  • Gaveau, B.; Moreau, M.; Tóth, J.: Variational nonequilibrium thermodynamics of reaction-diffusion systems. I. The information potential, Journal of Chemical Physics 111 (17) (1999), 7736-7747. manuscript.
  • Gaveau, B.; Moreau, M.; Tóth, J.: Variational nonequilibrium thermodynamics of reaction-diffusion systems. II. Path integrals, large fluctuations and rate constants, Journal of Chemical Physics 111 (17) (1999), 7748-7757. manuscript.
  • Gaveau, B.; Moreau, M.; Tóth, J.: Information potential and transition to criticality for certain two-species systems, Physica A 277 (3/4) (2000), 455-468. manuscript. manuscript.
  • Gaveau, B.; Moreau, M.; Tóth, J.: Scenarios for self-organized criticality in dynamical systems, Open Sys. & Information Dyn. 7 (4) (2000), 297--308. manuscript.
    We analyze the concept of Self-Organized Criticality in the case of dynamical systems, in particular for nonlinear reactive systems including arbitrary numbers of species and chemical reactions. We find mathematical conditions that allow for the existence of this behaviour. It is shown that these quite restrictive conditions can nevertheless be satisfied for physical reasons, in particular in chemical kinetics or population dynamics. It can be concluded that SOC, although apparently highly non-generic, should be observed in many natural dynamical systems. These results are applied for homogeneous and inhomogeneous catalytic chemical systems.
  • Gaveau, B.; Moreau, M.; Tóth, J.: Variational nonequilibrium thermodynamics of reaction-diffusion systems. III. Progress variables and dissipation of energy and information, Journal of Chemical Physics 115 (2) (2001), 680-690. manuscript.
  • Halász, G.; Tóth, J.; Hangos, K. M.: Energy-optimal operation conditions of a tunnel kiln, Computers and Chemical Engineering 12 (2/3) (1988), 183-187. *(1 independent citation)*
  • Halmschlager, A.; Szenthe, L.; Tóth, J.: Invariants of kinetic differential equations, Electronic Journal of the Qualitative Theory of Differential Equations, 14 (2004), 1-14.
    Polynomial differential equations showing chaotic behavior are investigated using polynomial invariants of the equations. This tool is more effective than the direct method for proving statements like the one: the Lorenz equation cannot be transformed into an equation which would be a mass action type kinetic model of a chemical reaction.
  • Hangos, K. M.; Tóth, J.: Maximum likelihood estimation of reaction-rate constants, Computers and Chemical Engineering 12 (2/3) (1988), 135-139. *(2 independent citations)*
  • Kiss, K.; Tóth, J.: n-dimensional ratio-dependent predator-prey systems with memory, Differential Equations and Dynamical Systems (in press)
    This paper deals with ratio-dependent predator-prey systems with delay. We will investigate under what conditions delay cannot cause instability in higher dimension. We give an example when delay causes instability.
    Mathematica programs to be read by MathematicaPlayer, to use by Mathematica 6.
  • Kovács, B.; Tóth, J.: Estimating reaction rate constants with neural networks, Enformatika. International Journal of Applied Mathematics and Computer Sciences 4 (2) (2007), 515--519. manuscript here.
  • Kovács, K.; Vizvári, B.; Riedel, M.; Tóth, J.: Decomposition of the permanganate/oxalic acid overall reaction to elementary steps based on integer programming theory, Physical Chemistry, Chemical Physics 6 (2004), 1236-1242. manuscript, data. *(2 independent citations)*
  • Kutas, T.; Tóth, J.: A stochastic model of phytoplankton dynamics in Lake Balaton, Journal of Statistical Computation and Simulation 21 (1985), 241-264. *(1 independent citations)*
  • Li, G., Rabitz, H., Tóth, J.: A general analysis of exact nonlinear lumping in chemical kinetics, Chem. Eng. Sci. 49 (3) (1994), 343-361. manuscript *(25 independent citations)*
  • Li, G.; Tomlin, A. S.; Rabitz, H.; Tóth, J.: Determination of approximate lumping schemes by a singular perturbation method, Journal of Chemical Physics 99 (5) (1993), 3562-3574. manuscript *(14 independent citations)*
  • Li, G.; Tomlin, A. S.; Rabitz, H.; Tóth, J.: A general analysis of approximate nonlinear lumping in chemical kinetics. I. Unconstrained lumping, Journal of Chemical Physics 101 (2) (1994), 1172-1187. *(13 independent citations)*
  • Nagy, I.; Póta, Gy.; Tóth, J.: Detailed balanced and unbalanced triangle reactions, Journal of Chemical Education (in press) (2007), -.
  • Nagy, I.; Kovács, B.; Tóth, J.: Detailed balance in ion channels: Applications of Feinberg's theorem, Reaction Kinetics and Catalysis Letters 96 (2) (2009), 263-267. manuscript here.
  • Rózsa, Z.; Tóth, J.: Exact linear lumping in abstract spaces, Electronic Journal of the Qualitative Theory of Differential Equations, 21 (2004), 1-20.
    Exact linear lumping has earlier been defined for a finite dimensional space, that is, for the system of ordinary differential equations y'=f o y as a linear transformation M for which there exists a function f^ such that y^:=My itself obeys a differential equation y^'=f^ o y^. Here we extend the idea for the case when the values of y are taken in a Banach space. The investigations are restricted to the case when f is linear. Many theorems hold for the generalization of exact lumping, such as necessary and sufficient conditions for lumpability, and relations between the qualitative properties of the original and the transformed equations. The motivation behind the generalization of exact lumping is to apply the theory to reaction-diffusion systems, to an infinite number of chemical species, to continuous components, or to stochastic models as well.
  • Schneider, K. R., Wegner, B., Tóth, J.: Qualitative analysis of as model for synaptic slow waves, J. Math. Chem. 1 (1987), 219-234.
  • Schuman, B.; Tóth J.: No limit cycle in two species second order kinetics, Bull. sci. math. 127 (2003), 222-230. manuscript. *(2 independent citations)*
  • Sipos, T.; Tóth, J.; Érdi, P.: Stochastic simulation of complex chemical reactions by digital computer, I. The model, Reaction Kinetics and Catalysis Letters 1 (1) (1974), 113-117. manuscript *(2 independent citations)*
  • Sipos, T.; Tóth, J.; Érdi, P.: Stochastic simulation of complex chemical reactions by digital computer, II. Applications, Reaction Kinetics and Catalysis Letters 1 (2) (1974), 209-213. manuscript *(2 independent citations)*
  • Szili, L., Tóth, J.: Necessary condition of the Turing instability, Phys. Rev. E 48 (1) (1993), 183-186. manuscript *(16 independent citations)*
  • Szili, L., Tóth, J.: On the origin of Turing instability, J. Math. Chem. 22 (1997), 39-53. manuscript *(2 independent citations)*
  • Szili, L.; Tóth, J.: Numerical and symbolic applications of Mathematica, Mathematica Pannonica 10 (1) (1999), 83-92.
  • Tomlin, A. S.; Li, G.; Rabitz, H.; Tóth, J.: A general analysis of approximate nonlinear lumping in chemical kinetics. II. Constrained lumping, Journal of Chemical Physics 101 (2) (1994), 1188-1201. *(17 independent citations)*
  • Tóth, J.: What is essential to exotic kinetic behaviour?, Reaction Kinetics and Catalysis Letters 9 (4) (1978), 377-381. manuscript *(5 independent citations)*
  • Tóth, J.: Gradient systems are cross-catalytic, Reaction Kinetics and Catalysis Letters 12 (3) (1979), 253-257. manuscript *(2 independent citations)*
  • Tóth, J.: Poissonian stationary distribution in a class of detailed balanced reactions, Reaction Kinetics and Catalysis Letters 18 (1-2) (1981), 169-173.
  • Tóth, J.: Elementa traktado de Wiener-filtrado, Matematiko Translimen 6 (1983), 21-23.
  • Tóth, J.: Bendixson-type theorems with applications, Zeitschrift für Angewandte Mathematik und Mechanik 67 (1) (1987), 31-35. *(5 independent citations)*
  • Tóth, J.: A functional equation related to random fields, Revue Roumaine de Mathématiques Pures et Appliquées 37 (3) (1992), 261-264.
  • Tóth, J.: On the equations of chemical kinetics, Nonlinear Vibration Problems-Zagadnenia Drgan Nieliniowych 25 (1993), 447-457.
  • Tóth, J.: Multistationarity is neither sufficient nor necessary to oscillation, Journal of Mathematical Chemistry 25 (4) (1999), 393-397. manuscript *(5 independent citations)*
  • Tóth, J., Hárs, V.: Orthogonal transforms of the Lorenz- and Rössler-equations, Physica 19D (1986), 135-144. manuscript.
    It is shown that none of the proper or improper orthogonal transformations transforms the Lorenz-equation into a kinetic equation, i.e. into an equation representing reasonable chemistry. It is also shown that none of the proper orthogonal transformations transforms a model by Rössler into a kinetic model either. The importance of the presence of negative cross-effects is hereby emphasized.
    *(13 independent citations)*
  • Tóth, J., Hárs, V.: Specification of oscillating chemical models starting form a given linearized form, Theor. Chim. Acta 70 (1986), 143-150. manuscript.
    The Lotka-Volterra model is shown to be the simplest unique model among those having the same linearized form. We also show that the two-dimensional Explodator is not unique in its own class: there are four models possessing the same linearized form. Finally, we propose a method for the construction of formal chemical models having prescribed properties (i. e. having prescribed a tzpe of one or more equilibrium points.)
    *(4 independent citations)*
  • Tóth, J., Li, G., Rabitz, H., Tomlin, A. S.: The effect of lumping and expanding on kinetic differential equations, SIAM J. Appl. Math. 57 (6) (1997), 1531-1556.
    manuscript. *(16 independent citations)*
  • Tóth, J.; Rospars, J.-P.: Dynamic modelling of biochemical reactions with applications to signal transduction: Principles and tools using Mathematica}, BioSystems, 79 (2005), 33-52.
    manuscript. *(1 independent citation)*
  • Tóth, J.; Szili, L.; Zachár, A.: Stability of polynomials, Mathematica in Education and Research 7 (2) (1998), 5-12. Zipped Mathematica notebook. *(1 independent citation)*
  • Tóth, J.; Török, T. L.: Poissonian stationary distribution: a degenerate case of stochastic kinetics, Reaction Kinetics and Catalysis Letters 13 (2) (1980), 167-171. manuscript *(1 independent citation)*
  • Tóth, J.; Ván, P.: Applying a list of functions to an argument: a dual of Map, Mathematica in Education and Research 9 (3/4) (2000), 58-63. Mathematica notebook.
  • Turányi, T.; Bérces, T.; Tóth, J.: The method of quasy-stationary sensitivity analysis, Journal of Mathematical Chemistry 2 (4) (1988), 401-409.
  • Turányi, T.; Tóth, J.: Comments to an article of Frank-Kamenetskii on the Quasi-Steady-State Approximation, Acta Chimica Hungarica-Models in Chemistry 129 (6) (1992), 903-914. *(5 independent citations)*
  • Papers in collections

    Book chapters

  • Gaveau, B.; Moreau, M.; Tóth, J.: Master equations and path-integral formulation of variational principles for reactions, In: Variational and Extremum Principles in Macroscopic Systems, Chapter 15, (S. Sienytucz, H. Farkas eds.), Elsevier, 2005, pp. 315--338. DVI PDF PostScript
    The mesoscopic nonequilibrium thermodynamics of a reaction-diffusion system is described by the master equation. The information potential is defined as the logarithm of the stationary distribution. The Fokker-Planck approximation and the Wentzel--Kramers--Brillouin method give very different results. The information potential is shown to obey a Hamilton-Jacobi equation, and from this fact general properties of this potential are derived. The Hamilton-Jacobi equation is shown to have a unique regular solution. Using the path integral formulation of the Hamilton-Jacobi approximation of the master equation it is possible to calculate rate constants for the transition from one well to another one of the information potential and give estimates of mean exit times. In progress variables, the Hamilton-Jacobi equation has always a simple solution which is a state function if and only if there exists a thermodynamic equilibrium for the system. An inequality between energy and information dissipation is studied, and the notion of relative entropy is investigated. A specific two-variable system and systems with a single chemical species are investigated in detail, where all the defined relevant quantities can be calculated explicitly.
  • Tóth, J.: On some problems of modelling in reaction kinetics, In: Bulletin of the University of Agricultural Sciences, 75th Anniversary Edition, Vol. II, Gödöllő, (Gy. Füleky, ed.) (1995-96), pp. 51-58.
  • Tóth, J.; Szili, L.; Érdi, P.: Chemical reaction kinetics as a prototype of nonlinear science, In: The Paradigm of Self-Organization II, (London) (G.J. Dalenoort ed.), Gordon and Breach, 1994, pp. 184-201.
  • Papers in conference proceedings

  • Érdi, P.; Grőbler, T.; Tóth, J.: On the classification of some classification problems, In: International Symposium on Information Physics, (Iizuka, Fukuoka, Japan) Kyushu Institute of Technology, 1993, pp. 110-117.
  • Érdi, P.; Réti, P.; Tóth, J.: Some investigations in qualitative reaction kinetics, In: Proceedings of the Congres International "Contribution des Calculateurs electroniques au developpement du Genie Chimique et de la Chemie Industrielle", (Paris, du 7 au 10 Mars, 1978) 1978, pp. 43-47.
  • Érdi, P.; Tóth, J.: On the theory of reacting mixtures, In: Proceedings of the Third Conference on Applied Chemistry. Unit Operations and Processes, (Veszprém, Hungary, 29-31 Aug. 1977) 1977, pp. 1-8.
  • Érdi, P.; Tóth, J.: Oscillatory phenomena at the synapse, In: Advances in Physiological Sciences, (Satellite Conference to the XXVIII International Congress of Physiological Sciences, Budapest, July 13-19, 1980) Mathematical and Computational Methods in Physiology (L. Fedina, B. Kanyár, B. Kocsis, M. Kollai eds.), 34 Pergamon Press - Akadémiai Kiadó, Budapest, 1981, pp. 113-121. *(1 independent citation)*
  • Érdi, P.; Tóth, J.: Anomalous stochastic kinetics, In: Chemical Reactivity in Liquids. Fundamental Aspects, (Paris, Sept. 7-11, 1987) (M. Moreau and P. Turq eds.), Plenum Press, New York and London, 1988, pp. 511-516.
  • Érdi, P.; Tóth, J.: Molecular computation: a dynamic approach, In: COMBIO'94 (Summer workshop on the computational modelling in biosciences), (Nyíregyháza, 1994.08.23) (I. Erényi, I. Molnár, K. Tarnay eds.), RÍM Kiadó, Nyíregyháza, 1994, pp. 41-52.
  • Érdi, P.; Tóth, J.: Towards a dynamic neuropharmacology: Integrating network and receptor levels, In: Brain, Vision and Artifical Intelligence, (M. De Gregorio, V. Di Maio, M. Frucci and C. Musio eds.), Lecture Notes in Computer Science 3704, Springer Verlag, Berlin, Heidelberg, 2005, pp. 1-14. .pdf file.
  • Érdi, P.; Tóth, J.; Hárs, V.: Some kinds of exotic phenomena in chemical systems, In: Colloquia Mathematica Societatis János Bolyai, (Szeged, Hungary, 1979) Qualitative Theory of Differential Equations (M. Farkas ed.), 30 North-Holland - János Bolyai Mathematical Society, Budapest, 1981, pp. 205-229. *(1 independent citation)*
  • Garay, M. B.; Csikja, R.; Tóth, J.: Some chaotic properties of the beta-hysteresis transformation, Proc. of the 2008 International Symposium on Nonlinear Theory and its Applications, Danubius Health Spa Resort Helia, Budapest, Republic of Hungary, September 7-10, 2008, pp. 191-194.
    A two-valued piecewise-linear, constant slope, 1D transformation is defined as a simplified model for hysteresis. By using Góra's S-matrix and classical results on Rényi's beta-transformation x|-->beta x (mod 1) the density function of the induced absolutely continuous ergodic measure is determined. Interesting simulation results reveal the chaos established.
  • Gaveau, B.; Moreau, M.; Tóth, J.: Path integrals and non-equilibrium thermodynamics, In: Path integrals from peV to TeV, (Florence, 1998), World Sci. Publishing, River Edge, NJ, 1999, pp. 52-58.
  • Halmschlager, A.; Tóth, J.: Über Theorie und Anwendung von polynominalen Differentialgleichungen, In: Wissenschaftliche Mitteilungen der 16. Frühlingsakademie, ISBN 963 214 1180, Mai 19-23, 2004, München-Wildbad Kreuth, Deutschland. Technische und Wirtschaftswissenschaftliche Universit\"at Budapest, Institut f\"ur Ingenieurweiterbildung, Budapest, 2004, pp. 35--40. doc file, pdf file.
    Polynomial equations so important in different fields of applications, especially in chemistry, are investigated. The literature is reviewed with the aim of possible applications of pure mathematical results in the field of chemical kinetics. Finally an example is treated in detail showing how to transform a mass action type kinetic equation into a homogeneous quadratic mass action type kinetic equation. The problem of transforming back is also discussed.
  • Hangos, K. M.; Tóth, J.: Maximum likelihood estimation of reaction rate constants, In: Proceedings of the MATCHEM, (Conference on Mathematical Methods in Chemical Engineering, Balatonfüred, Hungary, 5-8 May, 1986) Hungarian Chemical Society, Budapest, 1986, pp. 183-188.
  • Hárs, V.; Tóth, J.: On the inverse problem of reaction kinetics, In: Colloquia Mathematica Societatis János Bolyai, (Szeged, Hungary, 1979) Qualitative Theory of Differential Equations (M. Farkas ed.), 30 North-Holland - János Bolyai Mathematical Society, Budapest, 1981, pp. 363-379.
    The induced kinetic differential equations of reactions with mass action type kinetics are characterized within the class of polynomial differential equations: it is shown that a polynomial differential equation is kinetic if and only if it contains no negative cross effect. A constructive proof is given to prove sufficiency of the condition.
    *(12 independent citations)*
  • Hárs, V.; Tóth, J.; Érdi, P.; Hámori, J.: A formal dynamic model of the development of Purkinje dendritic spines, In: Advances in Physiological Sciences, (Satellite Conference to the XXVIII International Congress of Physiological Sciences, Budapest, July 13-19, 1980) Mathematical and Computational Methods in Physiology (L. Fedina, B. Kanyár, B. Kocsis, M. Kollai eds.), 34 Pergamon Press - Akadémiai Kiadó, Budapest, 1981, pp. 239-243.
  • Kutas, T.; Tóth, J.: Stochastic and deterministic approach to modelling a lake ecosystem, In: Proceedings of Simulation of Systems in Biology and Medicine, (SYSI '83, Prague, 1983) 1983.
  • Kutas, T.; Tóth, J.: Simulation of a lake ecosystem using deterministic and stochastic models, In: SIMULA Information, (Proceedings of the Twelfth SIMULA User's Conference, Budapest, 29-31 Aug. 1984) Norwegian Computing Center, Oslo, 1984, pp. 107-110.
  • Tóth, J.: A mass action kinetic model of neurochemical transmission, In: Dynamic Phenomena in Neurochemistry and Neurophysics: Theoretical Aspects, (Budapest, Aug. 21-23, 1984) (P. Érdi ed.), MTA KFKI, Budapest, 1985, pp. 52-55. *(4 independent citations)*
  • Tóth, J.: Notes on coexistence, In: Proceedings of the 11th International Conference on Nonlinear Oscillations, (Budapest, Aug. 17-23, 1987) (M. Farkas, V. Kertész, G. Stépán eds.), János Bolyai Mathemetical Society, Budapest, 1987, pp. 844-847.
  • Tóth, J.: Structure of the state space in stochastic kinetics, In: Proceedings of the 5th Pannonian Symposium on Mathematical Statistics, (Visegrád, Hungary, 1985) (W. Grossman, J. Mogyoródi, I. Vincze, W. Wertz eds.), János Bolyai Mathematical Society, Budapest, 1987, pp. 361-369.
  • Tóth, J.: Contribution to the general treatment of random processes used in chemical reaction kinetics, In: Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, (Prague, July 7-11, 1986) Academia (Publishing House of the Czechoslovak Academy of Sciences), Prague, 1988, pp. 373-379.
  • Tóth, J.: Formal Kinetics with Applications, 6th World Multiconference on Systemics, Cybernetics and Informatics (July 14-18, 2002, Orlando, FL, USA), Vol. XI (Computer Science II) (N. Callaos, M. Morgenstern and B. Sanchez eds.), pp. 573-576. Mathematica notebook.
  • Tóth, J.; Brochot, C., Bois, F.: Lumping in toxicokinetics, Poster presented at the ESF REACTOR workshop "Nonlinear phenomena in chemistry" Budapest, 24-27 Jan. 2003. poster.
  • Tóth, J.; Érdi, P.: On the theory of "pure" reaction kinetics, In: Proceedings of the Third Conference on Applied Chemistry. Unit Operations and Processes, (Veszprém, Hungary, 29-31 Aug. 1977) 1977, pp. 71-76.
  • Tóth, J.; Érdi, P.: Determination of reaction rate constants of complex chemical reactions from equilibrium fluctuations, In: Proceedings of the 5th Symposium on Computers in Chemical Engineering, (Czechoslovakia, 5-9 Oct. 1977) 1977, pp. 321-324. *(1 independent citations)*
  • Tóth, J.; Érdi, P.: Kinetic symmetries: Some hints, In: Chemical Reactivity in Liquids. Fundamental Aspects, (Paris, Sept. 7-11, 1987) (M. Moreau and P. Turq eds.), Plenum Press, New York and London, 1988, pp. 517-522.
  • Tóth, J.; Érdi, P.; Sipos, T.: Stochastic simulation of complex chemical reactions by digital computer, In: Proceedings of the 2nd Symposium on Computers in Chemical Engineering, (Ústí nad Labem, Czechoslovakia, Nov. 1973) 1973, pp. 83-89.
  • Tóth, J.; Halász, G. Gy.: Estimation of tunnel kiln parameters, In: Proceedings of the 8th IFAC/IFORS Symposium on Identification and System Parameter Estimation, (Beijing, 27-31 Aug. 1988) (Han-Fu Chen ed.), IFAC by Pergamon Press, China, 1988, pp. 1559-1563.
  • Tóth, J.; Hangos, K. M.; Halász, G. Gy.: Energy-optimal operation conditions of a tunnel kiln, In: Proceedings of the MATCHEM, (Conference on Mathematical Methods in Chemical Engineering, Balatonfüred, Hungary, 5-8 May, 1986) Hungarian Chemical Society, Budapest, 1986, pp. 435-442.
  • Tóth, J.; Kovács, K.; Vizvári, B.; Riedel, M.: Computer assisted study of the mechanism of the permanganate/oxalic acid reaction, Poster presented at the ESF REACTOR workshop "Nonlinear phenomena in chemistry" Budapest, 24-27 Jan. 2003. poster.
  • Tóth, J.; Kutas, T.; Csáki, P.: Estimation and prediction in a stochastic lake eutrophication model, In: Proceedings of Simulation of Systems in Biology and Medicine, (SYSI '84, Prague, 1984) 1984.
  • Tóth, J.; Li, G.; Rabitz, H.; Tomlin, A. S.: Reduction of the number of variables in dynamic models, In: Complex Systems in Natural and Economic Sciences, (Mátrafüred, 19-22 September, 1995.) (K. Martinás, M. Moreau eds.), ELFT, Budapest, 1996, pp. 17-34. *(1 independent citations)*
  • Tóth, J.; Török, T. L.: Stationary distributions in stochastic kinetics, In: Advances in Physiological Sciences, (Satellite Conference to the XXVIII International Congress of Physiological Sciences, Budapest, July 13-19, 1980) Mathematical and Computational Methods in Physiology (L. Fedina, B. Kanyár, B. Kocsis, M. Kollai eds.), 34 Pergamon Press - Akadémiai Kiadó, Budapest, 1981, pp. 103-111.
  • Demonstrations

  • Csima, G.; Szirmai J.; Tóth, J.: Iso-Optic Curve of the Ellipse, from The Wolfram Demonstrations Project.
  • Kabai, S.; Tóth, J.: Jefferson National Expansion Memorial, from The Wolfram Demonstrations Project.
  • Kabai, S.; Tóth, J.: Building Frame with Catenary Roof Beams, from The Wolfram Demonstrations Project.
  • Kabai, S.; Tóth, J.: Maximum Size of Involute Gear Teeth, from The Wolfram Demonstrations Project.
  • Várdai, J., Tóth, J.: Hopf Bifurcation in the Brusselator, from The Wolfram Demonstrations Project.
  • A few recent lectures

  • Egri, E.; Tóth, J.: Symbolic lumping of some catenary, mamillary and circular compartmental systems, In: Book of Abstracts, MaCS'06: 6th Joint Conference on Mathematics and Computer Science, (Pécs, Hungary, July 12-15, 2006), p. 35.
  • Halmschlager, A.; Szenthe, L.; Tóth, J.: Invariants of kinetic differential equations, 7th Colloquium on the Qualitative Theory of Differential Equations, July 14-18, 2003, Szeged, Hungary, abstract, dvi file, pdf file.
  • Kiss, K., Tóth, J.: n-dimensional ratio-dependent predator-prey systems with memory, Poster, Second ESF FUNCDYN Conference on Functional Dynamics, Rothenburg ob der Tauber, Germany, 15 - 18 September 2008, p. 15. poster.
  • Rózsa, Z.; Tóth, J.: Exact linear lumping in abstract spaces, 7th Colloquium on the Qualitative Theory of Differential Equations, July 14-18, 2003, Szeged, Hungary, abstract.
  • Sipos-Szabó, E., Tóth, J., Pál, I., Zsély, I. Gy., Turányi, T., Csikász-Nagy, A.: Sensitivity analysis of a generic cell-cycle model, Poster, Second ESF FUNCDYN Conference on Functional Dynamics, Rothenburg ob der Tauber, Germany, 15-18 September 2008, p. 15. poster.
  • Szili, L.; Tóth J.: Asymptotically stable polynomials with Mathematica, In: Book of Abstracts, MaCS'06: 6th Joint Conference on Mathematics and computer Science, (Pécs, Hungary, July 12--15, 2006, p. 89
  • Tóth, J.: Old methods wanted: Applications of deterministic and stochastic formal reaction kinetics to systems biology, In: Large Scale Random Graph Methods for Modeling Mesoscopic Behavior in Biological and Physical Systems, August 28--September 4, Budapest, 2006.
  • Tóth J. (based upon joint work with Nagy, A. L. (BUTE), Papp, D. (Rutgers)): Detailed balance in the models of chirality (Investigating the dynamics of biological models using the Mathematica package ReactionKinetics, Modellezés az élettudományokban, A Magyar Tudomány Ünnepe, Syeged, 2010. december 3.
    Starting from a special model of chirality we show how the mathematical theory of formal reaction kinetics and  the  program  package based  on  it  can  be  utilized  when  analyzing  the  variations  of models. The speciality of the package is that it highly utilizes the advantages of Mathematica,  
  • it automatically writes down and numerically solves the kinetic differential equation,  
  • it can also simulate the usual stochastic model,   
  • it  calculates  the  graph-theoretic  and  linear  algebraic  quantities  which  allow  to deduce statements on the qualitative behavior of the concentration of the different species. 
  • Important or favorite publications by others in English

    Burger, M., Field, R.: Oscillations and travelling waves in chemical systems, Wiley, New York, 1985.

    Császár, A., Jicsinszky, L., Turányi, T.: Generation of model reactions leading to limit cycle behaviour, Reaction Kinetics and Catalysis Letters 18 (1/2), 65-71 (1981).

    Farkas, Gy.: Local controllability of reactions, Journal of Mathematical Chemistry 24 (1) (1998), 1-14.

    Farkas, Gy.: On local observability of reactions, Journal of Mathematical Chemistry 24 (1) (1998), 15-22.

    Farkas, Gy.: Kinetic lumping schemes, Chemical Engineering Science 54 (1999), 3909-3915.

    Garay, B. M.; Várdai, J.: Interpolation of dynamic equations on time scales, J. Difference Eq. Appl. 13 (8/-9) (2007), 847-854.

    Horváth, Zsófia: Effect of lumping on controllability and observability, Poster presented at the Colloquium on Differential and Difference Equations dedicated to Prof. František Neuman on the occasion of his 65th birthday, Brno, Czech Republic, September 4 - 6, 2002 manuscript.

    Horváth, Zsófia: Effect of lumping on controllability and observability, Journal of Mathematical Chemistry (in press)

    Hoyle, M. H.: Transformations - An introduction and a bibliography, Int. Stat. Rev. 41 (2), (1973), 203-223.

    Inselberg, A.: Don't panic ... just do it parallel! Computational Statistics 14 (1999), 53-77.

    Izsák, F.; Lagzi, I.: Simulation of Liesegang pattern formation using a discrete stochastic model, Chemical Physics Letters 371 321-326.

    Kirschner, I.; Bálint, Á.; Csikja, R.; Gyarmati, B.; Balogh, A.; Mészáros, Cs.: An approximate symbolic solution for convective instability flows in vertical cylindrical tubes, Journal of Physics A, Mathematical and Theoretical 40 (2007) 9361-9369.

    Kovács, B.: Rate based call gapping with priorities and fairness between traffic classes, IEEE Trans. Comm. (submitted)

    Kovács, B.; Szalay, M.; Imre, S.: Modelling and quantitative analysis of LTRACK - A novel mobility management algorithm, Mobile Information Systems 2 (1) (2006) 21-50.

    Kozma, R., Th.: Horosphere Packings of the (3, 3, 6) Coxeter Honeycomb in Three-Dimensional Hyperbolic Space, from The Wolfram Demonstrations Project.

    Ladics, T.: The analysis of the splitting error for advection-reaction problems in air pollution models, Időjárás -. (in press). manuscript and figures.

    Ladics, T.: Application of Operator Splitting to Solve Reaction Diffusion Equations, arXiv:1011.4810 manuscript and figures.

    Ofella, P. (with Carl Woll): Robinson Tiling, from The Wolfram Demonstrations Project.

    Orlov, N. N., Rozonoer, L. I.: The macrodynamics of open systems and the variational principle of the local potential, J. Franklin Inst. 318(1984) 283-314 and 315-347.

    Papp, D., Vizvári, B.: Effective solution of linear Diophantine equation systems with an application in chemistry RUTCOR Research Reports 28-2004.

    Recski, A.: Calculus exercises with and without Mathematica, New Haven, 1995.

    Rényi, A.: Foundations of probability, Holden-Day Inc., San Francisco, Calif., 1970. ZBL 0203.49801, MR 41:9314.

    Scott, S. K.: Chemical Chaos, Oxford Univ. Press, 1991.

    Molnár, Z.; Nagy, I.; Szilágyi, T.: A change of variables theorem for the multidimensional Riemann integral, Ann. Univ. Sci. Eötvös, Sectio Math. (submitted)

    Tóth, Ágnes: Fast edge colouring of graphs, 2007 Wolfram Technology Conference.

    Turányi, T.: Sensitivity analysis of complex kinetic systems: Tools and applications, J. Math. Chem. 5 (1990) 203-248.

    Volpert, A. I., Hudjaev, S. I.: Analysis in classes of discontinuous functions and the equations of mathematical physics, Martinus Nijhoff Publ., Dordrecht, Boston, Lancaster, 1985.

    Wehrl, A.: General properties of entropy, Rev. Mod. Phys. 50 (2) (1978) 221-260.

    Zachár, A.: Comparison of transformations from nonkinetic to kinetic models, Acta Chimica Hungarica - Models in Chemistry 135 (3) (1998), 425-434.

    Zhang, S. Y.: Bibliography on Chaos, World Scientific, Singapore, New Jersey, London, Hong Kong, 1991.