Global Attractivity of Solutions of Nonlinear Delay Difference Equations

Abstract

Abstract The asymptotic behavior of solutions of delay difference equations is an important research topic in the field of qualitative analysis of difference equations and the key to grasp the evolution trend of various dynamic systems As we all know, most difference equations cannot find exact solutions Therefore, it is necessary to study the asymptotic behavior of the solution of the delay difference equation by indirect method. In this paper, improved the form of the equation in the existing reference, a single delay is changed into a multi delay equation, and the conditions required for the theorem to be established are weakened, so that the theorem can be applied to a wider range and still holds under the original conditions sufficient conditions for the asymptotic behavior of solutions independent of delay are obtained. The conclusion is proved by constructor method and counter proof method The relevant results in the existing literature are extended and improved to make the results more general. The results are applied to a kind of hematopoietic stem cell model. The asymptotic behavior of the solution is intuitively displayed in the form of chart to verify the conclusion.