具有恐惧效应和霍林 III 型功能响应的延迟扩散高斯型捕食者-猎物系统的全局霍普夫分岔

IF 2.6 4区数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY

Mathematical Modelling of Natural Phenomena Pub Date : 2024-02-16 DOI:10.1051/mmnp/2024003

Qian Zhang, Ming Liu, Xiaofeng Xu

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引用次数: 0

摘要

本文考虑了一个具有恐惧效应和霍林 III 型功能响应的延迟扩散捕食者-猎物系统，并对该系统施加了诺伊曼边界条件。首先，我们探讨了唯一正常数稳态的稳定性和局部霍普夫分岔的存在性。然后通过比较原理和迭代法得到系统 (4) 的全局吸引域 G∗。通过构建 Lyapunov 函数，我们研究了周期解的周期均匀有界性。最后，我们通过吴的全局霍普夫分岔定理证明了周期解的全局连续性。此外，我们还给出了一些支持分析结果的数值模拟。

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Global Hopf bifurcation of a delayed diffusive Gause-type predator-prey system with the fear effect and Holling type III functional response

In this paper, a delayed diffusive predator-prey system with the fear effect and Holling type III functional response is considered, and Neumann boundary condition is imposed on this system. First, we explore the stability of the unique positive constant steady state and the existence of local Hopf bifurcation. Then the global attraction domain G∗ of system (4) is obtained by the comparison principle and the iterative method. Through constructing the Lyapunov function, we investigate uniform boundedness of periodic solutions’periods. Finally, we prove the global continuation of periodic solutions by the global Hopf bifurcation theorem of Wu. Moreover, some numerical simulations that support the analysis results are given.

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来源期刊

Mathematical Modelling of Natural Phenomena MATHEMATICAL & COMPUTATIONAL BIOLOGY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

5.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The scope of the journal is devoted to mathematical modelling with sufficiently advanced model, and the works studying mainly the existence and stability of stationary points of ODE systems are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to the real world problems. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues. Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.