Open AccessGlobal population dynamics of a single species structured with distinctive time-varying maturation and self-limitation delays
Author(s) -
Chuangxia Huang,
Lihong Huang,
Jianhong Wu
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021138
Subject(s) - dynamics (music) , mathematics , stability (learning theory) , exponential stability , stability theory , constant (computer programming) , competition (biology) , population , control theory (sociology) , mathematical analysis , mathematical economics , computer science , physics , ecology , biology , artificial intelligence , control (management) , demography , nonlinear system , quantum mechanics , machine learning , sociology , acoustics , programming language
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.