Fractal Analysis and Control of a Type of Population Competition System

Abstract

The law of population quantity change is one of the issues of Animal Ecology and Resource Management. By studying the changes of population quantity, we can effectively grasp the population dynamics and living habits, which is of great significance for the rational utilization of resources and the protection of ecology. In recent years, biomathematics has been continuously developed, and its models have been well used. When people study populations, the most important question is whether the populations have a positive equilibrium state and whether this equilibrium state can remain stable. Mathematically, the population equilibrium state is about the stability of the solution of the population competition model. In this paper, we discuss the competition model of two groups from the perspective of fractal theory. We first apply the ideas and methods of Julia set in fractal geometry to the population competition model, and establish the Julia set of the competition model, and discuss the conditions that make the model stable. At the same time, it adopts feedback control method to control it, so as to realize the transition from unstable to stable model.