Dynamics and bifurcations of a discrete-time prey-predator model with Allee effect on the prey population

IF 3.1 3区环境科学与生态学 Q2 ECOLOGY Ecological Complexity Pub Date : 2021-12-01 DOI:10.1016/j.ecocom.2021.100962

Z. Eskandari , J. Alidousti , Z. Avazzadeh , J.A. Tenreiro Machado

引用次数: 11

Abstract

This paper studies the dynamic behavior of a discrete-time prey-predator model. It is shown that this model undergoes codimension one and codimension two bifurcations such as transcritical, flip (period-doubling), Neimark-Sacker and strong resonances 1:2, 1:3 and 1:4. The bifurcation analysis is based on the numerical normal form method and the bifurcation scenario around the bifurcation point is determined by their critical normal form coefficients. The advantage of this method is that there is no need to calculate the center manifold and to convert the linear part of the map to a Jordan form. The bifurcation curves of fixed points under variation of one and two parameters are obtained, and the codimensions one and the two bifurcations on the corresponding curves are computed.

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具有Allee效应的离散食饵-捕食模型的动力学和分岔

研究了离散时间捕食-食饵模型的动态行为。结果表明，该模型经历了余维一分岔和余维二分岔，如跨临界分岔、翻转(周期加倍)分岔、neimmark - sacker分岔和强共振1:2、1:3和1:4分岔。分岔分析基于数值范式方法，分岔点周围的分岔场景由其临界范式系数决定。这种方法的优点是不需要计算中心流形，也不需要将映射的线性部分转换为约旦形式。得到了不动点在一个和两个参数变化下的分岔曲线，并计算了相应曲线上的余维数1和两个分岔。

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

Ecological Complexity 环境科学-生态学

CiteScore

7.10

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： Ecological Complexity is an international journal devoted to the publication of high quality, peer-reviewed articles on all aspects of biocomplexity in the environment, theoretical ecology, and special issues on topics of current interest. The scope of the journal is wide and interdisciplinary with an integrated and quantitative approach. The journal particularly encourages submission of papers that integrate natural and social processes at appropriately broad spatio-temporal scales. Ecological Complexity will publish research into the following areas: • All aspects of biocomplexity in the environment and theoretical ecology • Ecosystems and biospheres as complex adaptive systems • Self-organization of spatially extended ecosystems • Emergent properties and structures of complex ecosystems • Ecological pattern formation in space and time • The role of biophysical constraints and evolutionary attractors on species assemblages • Ecological scaling (scale invariance, scale covariance and across scale dynamics), allometry, and hierarchy theory • Ecological topology and networks • Studies towards an ecology of complex systems • Complex systems approaches for the study of dynamic human-environment interactions • Using knowledge of nonlinear phenomena to better guide policy development for adaptation strategies and mitigation to environmental change • New tools and methods for studying ecological complexity