Analysis Of The Properties Of Two Competing Species Under Perturbation

Based on the lotka-volterra system,this paper increases the disturbance term and analyzes the existence and stability of the perturbation system with the method of qualitative and stability of ordinary differential equations.In this paper,we discuss the stability of disturbance parameters in different ranges and compare them with the original system to analysis biological significance.This paper is divided into five chapters and mainly studies four parts:In the first part,we calculate the possible equilibrium point of LV system and perturbation system.In the second part,when LV system has the only positive equilibrium point,we analyze the existence of the equilibrium points of the perturbation system and the conditions to be met when,the five equilibrium points exist simultaneously.In the third part,we study the stability of the equilibrium point of the distur-bance system,which is the core of this paper.Firstly,we analyze the stability of each equilibrium point.Secondly,the relationship between stability and existence is analyzed.At last,We get the local phase diagram in different cases.In the forth part,we summarize the conclusion of this paper and give a biological explanation.