Regular and Chaotic Dynamics in Nonlinear Systems of Ordinary Differential Equations of Weidlich-Trubetskov Type

摘要

Weidlich's approach to the mathematical modeling of a wide class of various economic and social phenomena is to describe these phenomena in terms of two interacting niacrovariables x and y that can have cooperative or antagonistic influence on each other. Following [1, 2], we say that the variable x is cooperative with respect to the variable y if x tends to increase y if x itself is large and decrease y if x is small. But if the variable x suppresses the variable y if x itself is large and strengthens y for small x, then the variable x is said to be antagonistic with respect to the variable y. Moreover, it is assumed in Weidlich's models that the variables x and y are self-saturating; therefore, the interaction character chosen for them is a system of two ordinary differential equations with nonlinear right-hand sides of logistic type:Weidlich's approach to the mathematical modeling of a wide class of various economic and social phenomena is to describe these phenomena in terms of two interacting niacrovariables x and y that can have cooperative or antagonistic influence on each other. Following [1, 2], we say that the variable x is cooperative with respect to the variable y if x tends to increase y if x itself is large and decrease y if x is small. But if the variable x suppresses the variable y if x itself is large and strengthens y for small x, then the variable x is said to be antagonistic with respect to the variable y. Moreover, it is assumed in Weidlich's models that the variables x and y are self-saturating; therefore, the interaction character chosen for them is a system of two ordinary differential equations with nonlinear right-hand sides of logistic type.