Global Attractivity for Lasota–Wazewska-Type System with Patch Structure and Multiple Time-Varying Delays

Zhiwen Long,Yanxiang Tan

doi:10.1155/2020/1947809

Abstract

This paper aims to study the asymptotic behavior of Lasota–Wazewska-type system with patch structure and multiple time-varying delays. Based on the fluctuation lemma and some differential inequality techniques, we prove that the positive equilibrium is a global attractor of the addressed system with small time delay. Finally, we provide an example to illustrate the feasibility of the theoretical results.

Highlights

In 1988, in order to describe the survival of red blood cells in animals, Wazewska–Czyzewska and Lasota in [1] presented the following delayed di erential equation model ὔ( ) = − ( ) + − ( − ( )), (1)=1 where ( ) represents the number of red blood cells at time, denotes the death rate of red blood cells, and are related to the production of red blood cells per unit time, ( ) represents the time required to produce a red blood cell
Since the model was proposed, there have been a large number of results about the dynamical behaviors for (1) and its modi cations due to their comprehensive practical application background
As far as we know, fewer works have been done concerning with the e ect of time delay on dynamical behaviors of Lasota– Wazewska-type model with patch structure. e purpose of the present paper is to establish some su cient conditions to guarantee the global attractivity of the following Lasota– Wazewska-type delay system with patch structure ὔ( ) = −δ ( ) +

Summary

Introduction

E purpose of the present paper is to establish some su cient conditions to guarantee the global attractivity of the following Lasota– Wazewska-type delay system with patch structure ὔ( ) = −δ ( ) + We further assume that there exists at least one positive constant ∗ = Is the positive equilibrium point of (2) satisfying 2. Global Attractivity of the Positive Equilibrium Point 1∗, 2∗, .

Results

Conclusion