The Systems Complexity Problem for Nonlinear Polynomial Discrete Systems with Many Delays and two Components. An Algebraic Approach

摘要

By the means of special operators and operations, the so-called D-operators and the star-product, a special algebraic description for nonlinear polynomial discrete systems in two dimensions is developed. By using this description, we can check if these nonlinear systems are “similar”or “equivalent” with linear systems, in the sense that the evolution of both systems, under the same initial conditions, are related among each other. Different kind of solutions of the problem, seem to determine different degrees of complexity for the original nonlinear systems. The whole approach has algebraic and algorithmic nature and no analytical tools are used.