The Boundedness And Limit Cycle For A Class Of Cubic Kolmogorov Type System

In this paper, we study the bounded cubic Kolmogorov type system.This paper is divided into three chapers.The first chapter is introduction. In the second chapter,we obtain the necessary and sufficient condition where the cubic Kolmogorov type system is bounded if homogeneous polynomials of degree 3 are relatively prime. And we obtain there are only four behaviours of the trajectories near the equator of the bounded cubic system if the homogeneous polynomials of degree 3 are relatively prime. In the third chapter,we study the existence and nonexistence of limit cycle for a class of bounded cubic systems.