New results on global exponential stability for a periodic Nicholson\u2019s blowflies model involving time-varying delays

Qian Cao,Chaofan Qian,Guoqiu Wang

doi:10.1186/s13662-020-2495-4

Abstract

This paper investigates a periodic Nicholson’s blowflies equation with multiple time-varying delays. By using differential inequality techniques and the fluctuation lemma, we establish a criterion to ensure the global exponential stability on the positive solutions of the addressed equation, which improves and complements some existing ones. The effectiveness of the obtained result is illustrated by some numerical simulations.

Highlights

1 Introduction Recently, the global exponential stability of positive periodic solutions and almostperiodic solutions for the famous Nicholson’s blowflies equation with multiple timevarying delays: m x (t) = –β(t)x(t) + αj(t)x t – σj(t) e–γj(t)x(t–σj(t)), j=1 t ≥ t0, (1.1)
The global exponential stability of positive periodic solutions and almostperiodic solutions for the famous Nicholson’s blowflies equation with multiple timevarying delays:m x (t) = –β(t)x(t) + αj(t)x t – σj(t) e–γj(t)x(t–σj(t)), j=1 t ≥ t0, (1.1)has been intensively studied in [1–3]
There are no research works on the global exponential stability of periodic solutions for Nicholson’s blowflies equation (1.1)

Summary

Introduction

1 Introduction Recently, the global exponential stability of positive periodic solutions and almostperiodic solutions for the famous Nicholson’s blowflies equation with multiple timevarying delays: m x (t) = –β(t)x(t) + αj(t)x t – σj(t) e–γj(t)x(t–σj(t)), j=1 t ≥ t0, (1.1) There are no research works on the global exponential stability of periodic solutions for Nicholson’s blowflies equation (1.1) Β ν(t) x ν(t) ≥ αj ν(t) x ν(t) – σj ν(t) e–γj(ν(t))x(ν(t)–σj(ν(t))), where ν(t) > t0, j ∈ Π , which, together with the fact that limt→+∞ x(ν(t)) = 0, suggests that lim x t→+∞

Results

Conclusion