Complex Dynamics of a Memory-Induced Stage-Structured Diffusive System With Maturation Delay and Strong Allee Effect

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-05 DOI:10.1002/mma.10664

Luhong Ye, Hongyong Zhao, Xuebing Zhang, Daiyong Wu

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Abstract

In this work, a memory-induced stage-structured prey–predator diffusive system with maturation delay and strong Allee effect is proposed. First, the positivity of solutions and survival of the non-spatial system are studied. The results indicate that strong Allee effect affects the coexistence of two populations to maintain the harmonious development of the ecosystem, and they can coexist if and only if the predator's fertility is greater than its mortality when the prey reaches its peak. The non-spatial system can undergo Hopf bifurcation caused by the maturation delay. Then we obtain complex dynamics for the spatial system with spatial memory. On one hand, spatial memory diffusion and memory delay can bring about not only Hopf bifurcation and Turing bifurcation but also Turing-Hopf bifurcation and Bogdanov-Takens bifurcation with strong Allee effect. On the other hand, spatial memory delay and maturation delay could induce double Hopf bifurcation. Furthermore, we also investigate the global continuation of local periodic solutions for the spatial system without spatial memory. These interesting results may provide new clues for the investigation of the coexistence for the populations and understanding the complex dynamics of prey–predator systems.

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具有成熟延迟和强通道效应的记忆诱导阶段结构扩散系统的复杂动力学

本文提出了一种具有成熟延迟和强Allee效应的记忆诱导阶段结构捕食扩散系统。首先，研究了非空间系统解的正性和生存性。结果表明，强烈的Allee效应影响着两个种群的共存，以维持生态系统的和谐发展，当且仅当捕食者的繁殖力大于被捕食者的死亡率达到峰值时，它们才能共存。成熟延迟导致非空间系统发生Hopf分岔。然后得到具有空间记忆的空间系统的复杂动力学。一方面，空间记忆扩散和记忆延迟不仅会导致Hopf分岔和Turing分岔，还会导致具有强烈Allee效应的Turing-Hopf分岔和Bogdanov-Takens分岔。另一方面，空间记忆延迟和成熟延迟可诱发双Hopf分岔。此外，我们还研究了无空间记忆的空间系统局部周期解的全局延拓问题。这些有趣的结果可能为研究种群的共存和理解捕食系统的复杂动态提供新的线索。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.