A new theoretical approach and mathematical model for the simulation of the dynamic behavior of complex systems are presented. Chemical reaction dynamics are used as a basis for the mathematical modeling of the dynamics of living systems. The meaning of discrete time and space appearing in the new equations are discussed. Some numerical results of a new mathematical model for simulation of the oscillatory and spatial dynamic behavior of physicochemical reactions are given. The proposed theoretical and mathematical tools are considered as the beginning of the development of a 'calculus of iterations' and difference equations in addition to the 'calculus of infinitesimal' and differential equations for the mathematical modeling of non-linear dynamics.