Discrete Dynamics in Nature and Society
Volume 1 (1997), Issue 1, Pages 31-43
Theoretical foundation for the discrete dynamics of physicochemical systems: Chaos, self-organization, time and space in complex systems
International Group for Scientific and Technological Chaos Studies, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, Israel
Received 9 October 1996
Copyright © 1997 V. Gontar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A new theoretical foundation for the discrete dynamics of physicochemical systems is presented. Based on the analogy between the -theorem of the theory of dimensionality, the second law of thermodynamics and the stoichiometry of complex physicochemical reactions, basic dynamic equations and an extreme principle were formulated. The meaning of discrete time and space in the proposed equations is discussed. Some results of numerical calculations are presented to demonstrate the potential of the proposed approach to the mathematical simulation of spatiotemporal physicochemical reaction dynamics.