Positioned spread models: A mathematical analysis of the topological and random population systems.

Abstract

Considering limited environmental resources, this article develops topological and random population systems, as well as positioned spread models that emphasize spatial distribution and growth. It incorporates key factors such as the birth rate and migration rate to analyze the population's spatial dynamics using tools from dynamical systems and probability theory. In addition, numerical examples and simulation results are provided to validate the theory for both topological and random models.