Positive periodic solution for Nicholson\u2019s blowfies systems with patch structure

Feng Duan,Bo Du

doi:10.1186/s13662-020-02714-w

Abstract

A generalized Nicholson blowfies system with patch structure is studied. Some existence and asymptotic stability results of the positive periodic solution to the considered system are obtained by coincidence degree theory and some analysis techniques. Finally, two examples are given to show the effectiveness of the results in the present paper.

Highlights

In 1980, Gurney et al [1] studied the delayed Nicholson blowflies equation x (t) = Px(t – τ )e–αx(t–τ) – γ x(t), (1.1)where x(t) represents the population of mature adults at time t,1 α denotes the population size at which the complete population reproduces at its maximum rate, P denotes the maximum possible per capita egg production rate, τ > 0 is a delay term, γ > 0 is the mortality rate
The existence and stability of positive periodic solutions of population dynamic systems belong to the important issues in differential dynamic systems
By the use of topology degree theory, some sufficient conditions are obtained to guarantee the existence of positive periodic solutions of the considered model

Summary

Introduction

By the use of topology degree theory, some sufficient conditions are obtained to guarantee the existence of positive periodic solutions of the considered model. Based on coincidence degree theory, the authors obtained some sufficient conditions for the existence of positive periodic solutions to the considered model. Li and Du [7] obtained the existence of positive periodic solutions for a Nicholson blowflies model with multiple delays by using the Krasnoselskii cone fixed point theorem. Chen and Liu [8] obtained the existence and dynamic properties of positive almost periodic solutions for the generalized Nicholson blowflies equation with multiple delays and derived some conditions to ensure that the solutions of the considered model converge locally exponentially to a unique equilibrium point.

Conclusions and discussions

Methods