The Boundedness of the Solution of a Class of Biological Population Models

Abstract

In biological models, the equilibrium solution is a bounded positive solution, which has very important practical significance. In this paper, a class of nonlinear delay difference equations is proposed, which is applicable to a variety of common biological population models, such as Nicholson’s blowflies and hematopoietic stem cell models. This article is to discuss this kind of nonlinear delay difference equation boundedness of the solution of the equilibrium, in the existing literature, this paper studies the nonlinear delay difference equation of the existence of bounded positive solutions of thought method, using structure function method and reduction to absurdity proved the existence of positive solutions of the equation, a class of nonlinear delay difference equation is obtained sufficient conditions for the existence of bounded positive solutions of, and proof is given. It is proved that the equilibrium solution of the nonlinear delay difference equation is always a bounded positive solution if the function f(x) is monotonically decreasing function or unimodal function and the function g(x) is monotonically increasing function. The relevant results of the existing literature are generalized and improved to make the results more general.