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Variational problems associated with a system of nonlinear Schrödinger equations with three wave interaction

## Global population dynamics of a single species structured with distinctive time-varying maturation and self-limitation delays

 1 School of Mathematics and Statistics, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, China 2 Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada

* Corresponding author: Jianhong Wu

Received  September 2020 Revised  February 2021 Published  May 2021

Fund Project: This work was supported by the National Natural Science Foundation of China (No. 11971076), the Natural Sciences and Engineering Research Council of Canada, and the Canada Research Chairs program

We consider the classical Nicholson's blowflies model incorporating two distinctive time-varying delays. One of the delays corresponds to the length of the individual's life cycle, and another corresponds to the specific physiological stage when self-limitation feedback takes place. Unlike the classical formulation of Nicholson's blowflies equation where self-regulation appears due to the competition of the productive adults for resources, the self-limitation of our considered model can occur at any developmental stage of an individual during the entire life cycle. We aim to find sharp conditions for the global asymptotic stability of a positive equilibrium. This is a significant challenge even when both delays are held at constant values. Here, we develop an approach to obtain a sharp and explicit criterion in an important situation where the two delays are asymptotically apart. Our approach can be also applied to the non-autonomous Mackey-Glass equation to provide a partial solution to an open problem about the global dynamics.

Citation: Chuangxia Huang, Lihong Huang, Jianhong Wu. Global population dynamics of a single species structured with distinctive time-varying maturation and self-limitation delays. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021138
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##### References:
Numerical solutions $x(t)$ to (17) with the two delays $h(t)$ and $g(t)$ given by (18) and different initial values $6$, $15$, $20$
Numerical solutions $x(t)$ to (17) with delays given in (19) and different initial values $5$, $17$, $30$
Numerical solutions $x(t)$ to (17) with delays given in (20) and different initial values $6$, $15$, $20$
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