Theoretical foundation for the discrete dynamics of physicochemical systems: Chaos, self-organization, time and space in complex systems

Abstract

A new theoretical foundation for the discrete dynamics of physicochemical systems is presented. Based on the analogy between the π-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.

Keywords

• Chaos
• Discrete dynamics
• Chemical reaction dynamics
• Complexity.