Almost periodic solutions for a delayed Nicholson’s blowflies system with nonlinear density-dependent mortality terms and patch structure

Wei Chen,Wentao Wang

doi:10.1186/1687-1847-2014-205

Abstract

We study positive almost periodic solutions for a delayed Nicholson’s blowflies system with nonlinear density-dependent mortality terms and patch structure. By applying the differential inequality technique and the Lyapunov functional, we derive sufficient conditions for the existence and global exponential stability of positive almost periodic solutions. We also give an example and its numerical simulations to support the theoretical effectiveness.

Highlights

As far as we know, there exist few works on the global exponent stability of positive almost periodic solutions for a Nicholson’s blowflies system with nonlinear densitydependent mortality terms and patch structure
To describe the population of Australian sheep-blowfly and agree well with the experimental data of Nicholson [ ], Gurney et al [ ] proposed the following famous Nicholson’s blowflies equationN (t) = –δN(t) + pN(t – τ )e–aN(t–τ). ( . )Here, N(t) is the size of the population at time t, p is the maximum per capita daily egg production,a is the size at which the population reproduces at its maximum rate, δ is the per capita daily adult death rate, and τ is the generation time
Motivated by the above arguments, in this paper, we investigate the existence and global exponential stability of positive almost periodic solutions for the following delayed Nicholson’s blowflies system with nonlinear density-dependent mortality terms and patch structure: n

Summary

Introduction

As far as we know, there exist few works on the global exponent stability of positive almost periodic solutions for a Nicholson’s blowflies system with nonlinear densitydependent mortality terms and patch structure. Motivated by the above arguments, in this paper, we investigate the existence and global exponential stability of positive almost periodic solutions for the following delayed Nicholson’s blowflies system with nonlinear density-dependent mortality terms and patch structure: n Where aij, bij, cim, γim : R → ( , +∞) and τim : R → R+ are continuous almost periodic functions with i, j ∈ := { , , .

Results

Conclusion