{"title":"Complex dynamical properties and chaos control for a discrete modified Leslie-Gower prey-predator system with Holling II functional response","authors":"Mianjian Ruan, Xianyi Li","doi":"10.1186/s13662-024-03828-1","DOIUrl":null,"url":null,"abstract":"<p>In this study, the semi-discretization technique is employed to establish a discrete representation of a modified Leslie-Gower prey-predator system that includes a Holling II type functional response. The dynamics of this model are then analyzed through the application of center manifold theory and bifurcation theory. We present comprehensive results for the local stability of the fixed points across the entire parameter space. Additionally, we provide sufficient conditions for the occurrence of flip bifurcation and Neimark-Sacker bifurcation. Besides, the system has experienced a flip bifurcation to chaos controlled using the method of chaos control, viz., state feedback method, pole placement technique, and hybrid control strategy. Furthermore, we provide specific conditions to ensure that bifurcation and chaos can be stabilized. Finally, numerical simulations are conducted to validate theoretical analysis and illustrate several new complex dynamical behaviors between two species.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Difference Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13662-024-03828-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, the semi-discretization technique is employed to establish a discrete representation of a modified Leslie-Gower prey-predator system that includes a Holling II type functional response. The dynamics of this model are then analyzed through the application of center manifold theory and bifurcation theory. We present comprehensive results for the local stability of the fixed points across the entire parameter space. Additionally, we provide sufficient conditions for the occurrence of flip bifurcation and Neimark-Sacker bifurcation. Besides, the system has experienced a flip bifurcation to chaos controlled using the method of chaos control, viz., state feedback method, pole placement technique, and hybrid control strategy. Furthermore, we provide specific conditions to ensure that bifurcation and chaos can be stabilized. Finally, numerical simulations are conducted to validate theoretical analysis and illustrate several new complex dynamical behaviors between two species.
本研究采用半离散化技术建立了一个包含霍林 II 型功能响应的修正莱斯利-高尔猎物-捕食者系统的离散表示。然后应用中心流形理论和分岔理论分析了该模型的动力学。我们提出了整个参数空间内定点局部稳定性的综合结果。此外，我们还提供了发生翻转分岔和 Neimark-Sacker 分岔的充分条件。此外，利用混沌控制方法，即状态反馈方法、极点放置技术和混合控制策略，系统经历了翻转分岔到混沌控制。此外，我们还提供了确保分岔和混沌稳定的具体条件。最后，我们进行了数值模拟，以验证理论分析，并说明了两个物种之间的几种新的复杂动力学行为。
期刊介绍：
The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions.
The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between.
The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations.
Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.
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