Positive Periodic Solutions of Nicholson‐Type Delay Systems with Nonlinear Density‐Dependent Mortality Terms

Abstract

This paper is concerned with the periodic solutions for a class of Nicholson-type delay systems with nonlinear density-dependent mortality terms. By using coincidence degree theory, some criteria are obtained to guarantee the existence of positive periodic solutions of the model. Moreover, an example and a numerical simulation are given to illustrate our main results.

Existence and Global Exponential Stability of Positive Almost Periodic Solutions for a Delayed Nicholson's Blowflies Model

“…For all we know, there is no research on the problems of positive almost periodic solutions of Nicholson's blowflies model with a nonlinear density-dependent mortality term a(t)x(t) b(t)+x(t) . Thus, all the results in the references [2,4,5,6,11,12,13,14,15,17,18,21,24,28,32] and [3,19,27,30] cannot be applicable to prove that all the solutions of (4.1) with initial value ϕ ∈ C + and ϕ(0) > 0 converge exponentially to the positive almost periodic solution. Moreover, in this present paper, we give a novel proof to establish some criteria to guarantee the global exponential stability of almost periodic solutions for Nicholson's blowflies model with a nonlinear density-dependent mortality term.…”

“…More details on biological explanation to model (1.1) can be found in [1] and [28]. Subsequently, there have been extensive results in the literature on the most important qualitative properties of the model and its analogous equations such as existence of positive solutions, persistence, permanence, oscillation and stability; some of the results can be found in [2,4,11,14,17,29]. On the other hand, the variation of the environment plays an important role in many biological and ecological dynamical systems.…”

Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System

“…Recently, the study on Nicholson's blowflies type systems has attracted much attention (cf. [3][4][5][6][7][8] and references therein). In particular, several authors have made contribution on the existence of periodic solutions for Nicholson's blowflies type systems (see, e.g., [6,7]).…”

“…[3][4][5][6][7][8] and references therein). In particular, several authors have made contribution on the existence of periodic solutions for Nicholson's blowflies type systems (see, e.g., [6,7]). In addition, discrete Nicholson's blowflies type models have been studied by several authors (see, e.g., [9][10][11][12] and references therein).…”

New results on global asymptotic stability for a class of delayed Nicholson's blowflies model

“…Chen et. al , Hou , and Chen investigated the local existence of periodic solution problem for its generalized equations. More recently, Wang studied the local extinction of Nicholson's blowflies system with nonlinear density‐dependent mortality terms.…”