Stability on a patch structure Nicholson’s blowflies system involving distinctive delays

Xu, Yanli; Cao, Qian; Guo, Xiaojin

doi:10.1016/j.aml.2020.106340

Cited by 34 publications

(10 citation statements)

References 26 publications

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“…Motivated by the previous discussions, in this paper, without adopting the reduced order method, we shall install new results concerning the anti-periodic dynamics for HIHNNs with time-varying delays and continuously distributed delays. Some sufficient conditions ensuring the existence and global exponential stability on the anti-periodic solution of system (1.1) are established by using differential inequalities and the Lyapunov function method, which improve and complement some earlier publications [16,17,[36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 74%

Anti-periodicity on high-order inertial Hopfield neural networks involving mixed delays

Yao

Cao

2020

J Inequal Appl

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This paper deals with a class of high-order inertial Hopfield neural networks involving mixed delays. Utilizing differential inequality techniques and the Lyapunov function method, we obtain a sufficient assertion to ensure the existence and global exponential stability of anti-periodic solutions of the proposed networks. Moreover, an example with a numerical simulation is furnished to illustrate the effectiveness and feasibility of the theoretical results.

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Section: Introductionmentioning

confidence: 74%

Anti-periodicity on high-order inertial Hopfield neural networks involving mixed delays

Yao

Cao

2020

J Inequal Appl

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“…β j (t)x(t − h j (t))e −γj (t)x(t−gj (t)) , t ≥ t 0 , (3.11) where g j denotes the developmental or maturation time whereas h j represents the reproduction lag. Y. Xu et al [21] and X. Long [14] also established the global stability on the zero equilibrium point for classical Nicholson's blowflies models involving distinctive delays.…”

Section: Global Attractivity Of the Positive Equilibriummentioning

confidence: 98%

“…As [6,21,14], in [16,11], the authors still were unable to derive any global convergence for the positive equilibrium point of (1.2). Theorem 3.1 complements the aforementioned works and this seems to be the first time that such a result is derived for this type of Nichlson's blowflies equation.…”

Section: Global Attractivity Of the Positive Equilibriummentioning

confidence: 99%

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

Huang

2022

DCDS-B

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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.

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“…The birth function gets the maximum reproduction value with N = 1 N D . The delay Nicholson's blowflies equation offers a suitable benchmark for describing a 'humped' relationship between future recruitment and current population as it presents abundant dynamics characteristics, such as global attractivity, complex oscillations and even chaotic behaviour [2,9,10,14,21,23,25,29,31,36,39,42].…”

Section: Introductionmentioning

confidence: 99%

Global convergence dynamics of almost periodic delay Nicholson's blowflies systems

Huang

2020

Journal of Biological Dynamics

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We take into account nonlinear density-dependent mortality term and patch structure to deal with the global convergence dynamics of almost periodic delay Nicholson's blowflies system in this paper. To begin with, we prove that the solutions of the addressed system exist globally and are bounded above. What's more, by the methods of Lyapunov function and analytical techniques, we establish new criteria to check the existence and global attractivity of the positive asymptotically almost periodic solution. In the end, we arrange an example to illustrate the effectiveness and feasibility of the obtained results.

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Stability on a patch structure Nicholson’s blowflies system involving distinctive delays

Cited by 34 publications

References 26 publications

Anti-periodicity on high-order inertial Hopfield neural networks involving mixed delays

Anti-periodicity on high-order inertial Hopfield neural networks involving mixed delays

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

Global convergence dynamics of almost periodic delay Nicholson's blowflies systems

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