{"title":"Nonsmooth dynamics of a Filippov predator–prey ecological model with antipredator behavior","authors":"Lidong Huang, Wenjie Qin, Shuai Chen","doi":"10.1186/s13662-024-03808-5","DOIUrl":null,"url":null,"abstract":"<p>This article proposes a class of nonsmooth Filippov pest–predator ecosystems with intermittent control strategies based on the pest’s antipredator behavior. aiming to investigate the influence of control strategies and switching thresholds on pest control. First, a comprehensive theoretical analysis of various equilibria within the Filippov system is undertaken, emphasizing the presence and stability of sliding mode dynamics and pseudoequilibrium. Secondly, through numerical simulations, the article discusses boundary-focus, boundary-node, and boundary-saddle bifurcation. Finally, the nonexistence of limit cycles in the Filippov system is theoretically studied. The research indicates that the solution trajectories of the model ultimately stabilize either at the real equilibria or at pseudoequilibrium on the model’s switching surface. Moreover, when the model has multiple coexisting real equilibrium and pseudoequilibrium, the pest-control strategy is correlated with the initial density of both the pest and the predator population.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2024-05-10","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/s13662-024-03808-5","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
This article proposes a class of nonsmooth Filippov pest–predator ecosystems with intermittent control strategies based on the pest’s antipredator behavior. aiming to investigate the influence of control strategies and switching thresholds on pest control. First, a comprehensive theoretical analysis of various equilibria within the Filippov system is undertaken, emphasizing the presence and stability of sliding mode dynamics and pseudoequilibrium. Secondly, through numerical simulations, the article discusses boundary-focus, boundary-node, and boundary-saddle bifurcation. Finally, the nonexistence of limit cycles in the Filippov system is theoretically studied. The research indicates that the solution trajectories of the model ultimately stabilize either at the real equilibria or at pseudoequilibrium on the model’s switching surface. Moreover, when the model has multiple coexisting real equilibrium and pseudoequilibrium, the pest-control strategy is correlated with the initial density of both the pest and the predator population.
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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