Equilibrium and Stability of Entropy Operator Model for Migratory Interaction of Regional Systems

Abstract

In this paper, we develop a dynamic model for migratory interaction of regional systems that is based on an entropy operator. Next, we study the properties of this operator and establish the existence of a unique singular point in the dynamic entropy model. Here, we use monotonicity property of entropy operator on corresponding vector interval. We study Lyapunov stability of a dynamic system with entropy operator. Stability conditions have been obtained in terms of eigenvalues of linearized system's matrix. Finally, we give an illustrative example for migratory interaction of regional systems.

Soft Randomized Machine Learning Procedure for Modeling Dynamic Interaction of Regional Systems

“…Consider the dynamic discrete-time model of migratory interaction with shared resource constraints that is presented in [5]. The first sub-model represents migration flows within the system GF I and is described by the dynamic regression equation…”

“…All these characteristics are specified by the regions of both systems. The dimensionality of the parametric space is reduced using the same approach as in [5]. The whole essence is to assign a relative regional differentiation of all parameters except for the weights b 1 (mobility) and b 2 (internal migration) of these groups, which are considered as model variables.…”

“…The authors of [5] suggested a dynamic entropy model for the migratory interaction of regional systems. In comparison with biological reproduction, migration mobility is a rather fast process [1,6].…”

“…This paper studies a stochastic version of the model in [5], in which random parameters and measurement noises are characterized by probability density functions (PDFs). These functions are estimated using retrospective information on the real dynamics of regional population size with "soft" randomized machine learning [15].…”