Nonlinear dynamics of the predator – prey system in a heterogeneous habitat and scenarios of local interaction of species

IF 0.5 Q4 PHYSICS, MULTIDISCIPLINARY

Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika Pub Date : 2021-09-30 DOI:10.18500/0869-6632-2021-29-5-751-764

V. Tsybulin, T. D. Ha, P. Zelenchuk

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引用次数: 1

Abstract

The purpose of this work is to study the influence of various local models in the equations of diffusion–advection– reaction on the spatial processes of coexistence of predators and prey under conditions of a nonuniform distribution of the carrying capacity. We consider a system of nonlinear parabolic equations to describe diffusion, taxis, and local interaction of a predator and prey in a one-dimensional habitat. Methods. We carried out the study of the system using the dynamical systems approach and a computational experiment based on the method of lines and a scheme of staggered grids. Results. The behavior of the predator – prey system has been studied for various scenarios of local interaction, taking into account the hyperbolic law of prey growth and the Holling effect with nonuniform carrying capacity. We have established paradoxical scenarios of interaction between prey and predator for several modifications of the trophic function. Stationary and nonstationary solutions are analyzed considering diffusion and directed migration of species. Conclusion. The trophic function that considers the heterogeneity of the resource is proposed, which does not lead to paradoxical dynamics.

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异质生境中捕食-猎物系统的非线性动力学及物种局部相互作用

本文研究了在承载力分布不均匀的条件下，扩散-平流-反应方程中不同局部模型对捕食者和被捕食者共存空间过程的影响。我们考虑一个非线性抛物方程系统来描述一维栖息地中捕食者和猎物的扩散、趋向性和局部相互作用。方法。我们使用动力系统方法和基于线法和交错网格方案的计算实验对该系统进行了研究。结果。考虑猎物生长的双曲规律和承载能力不均匀的霍林效应，研究了捕食者-猎物系统在各种局部相互作用情况下的行为。我们已经建立了食饵和捕食者之间相互作用的矛盾情景，用于营养功能的几种修改。考虑物种的扩散和定向迁移，分析了平稳解和非平稳解。结论。提出了考虑资源异质性的营养函数，这不会导致矛盾的动力学。

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

Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika PHYSICS, MULTIDISCIPLINARY-

CiteScore

1.20

自引率

25.00%

发文量

期刊介绍： Scientific and technical journal Izvestiya VUZ. Applied Nonlinear Dynamics is an original interdisciplinary publication of wide focus. The journal is included in the List of periodic scientific and technical publications of the Russian Federation, recommended for doctoral thesis publications of State Commission for Academic Degrees and Titles at the Ministry of Education and Science of the Russian Federation, indexed by Scopus, RSCI. The journal is published in Russian (English articles are also acceptable, with the possibility of publishing selected articles in other languages by agreement with the editors), the articles data as well as abstracts, keywords and references are consistently translated into English. First and foremost the journal publishes original research in the following areas: -Nonlinear Waves. Solitons. Autowaves. Self-Organization. -Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos. -Applied Problems of Nonlinear Oscillation and Wave Theory. -Modeling of Global Processes. Nonlinear Dynamics and Humanities. -Innovations in Applied Physics. -Nonlinear Dynamics and Neuroscience. All articles are consistently sent for independent, anonymous peer review by leading experts in the relevant fields, the decision to publish is made by the Editorial Board and is based on the review. In complicated and disputable cases it is possible to review the manuscript twice or three times. The journal publishes review papers, educational papers, related to the history of science and technology articles in the following sections: -Reviews of Actual Problems of Nonlinear Dynamics. -Science for Education. Methodical Papers. -History of Nonlinear Dynamics. Personalia.