{"title":"DYNAMICS AND BLOW-UP CONTROL OF A LESLIE–GOWER PREDATOR–PREY MODEL WITH GROUP DEFENCE IN PREY","authors":"RAJESH RANJAN PATRA, SARIT MAITRA, SOUMEN KUNDU","doi":"10.1142/s0218339024500165","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we designed a population model that shows how a prey species defends itself against a generalist predator by exhibiting group defence. A non-monotonic functional response is used to represent the group defence functionality. We have demonstrated the model’s local stability in the vicinity of the coexisting equilibrium solution employing a local Lyapunov function. Condition for existence of Hopf bifurcation is obtained along with its normal form. The suggested model has been validated by numerical simulations, which have also been used to verify the acquired analytical results. The parameters are subjected to sensitivity analysis by utilizing partial rank correlation coefficient (PRCC) and Latin hypercube sampling (LHS). The <i>Z</i>-type dynamic method is used to prevent population blow-up.</p>","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Biological Systems","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1142/s0218339024500165","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BIOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we designed a population model that shows how a prey species defends itself against a generalist predator by exhibiting group defence. A non-monotonic functional response is used to represent the group defence functionality. We have demonstrated the model’s local stability in the vicinity of the coexisting equilibrium solution employing a local Lyapunov function. Condition for existence of Hopf bifurcation is obtained along with its normal form. The suggested model has been validated by numerical simulations, which have also been used to verify the acquired analytical results. The parameters are subjected to sensitivity analysis by utilizing partial rank correlation coefficient (PRCC) and Latin hypercube sampling (LHS). The Z-type dynamic method is used to prevent population blow-up.
在本文中，我们设计了一个种群模型，展示了猎物物种如何通过群防来抵御通性捕食者。该模型采用非单调函数反应来表示群体防御功能。我们利用局部 Lyapunov 函数证明了该模型在共存平衡解附近的局部稳定性。我们还获得了霍普夫分岔的存在条件及其正常形式。所建议的模型已通过数值模拟进行了验证，数值模拟也用于验证所获得的分析结果。利用部分秩相关系数（PRCC）和拉丁超立方采样（LHS）对参数进行了敏感性分析。采用 Z 型动态方法来防止群体膨胀。
期刊介绍：
The Journal of Biological Systems is published quarterly. The goal of the Journal is to promote interdisciplinary approaches in Biology and in Medicine, and the study of biological situations with a variety of tools, including mathematical and general systems methods. The Journal solicits original research papers and survey articles in areas that include (but are not limited to):
Complex systems studies; isomorphies; nonlinear dynamics; entropy; mathematical tools and systems theories with applications in Biology and Medicine.
Interdisciplinary approaches in Biology and Medicine; transfer of methods from one discipline to another; integration of biological levels, from atomic to molecular, macromolecular, cellular, and organic levels; animal biology; plant biology.
Environmental studies; relationships between individuals, populations, communities and ecosystems; bioeconomics, management of renewable resources; hierarchy theory; integration of spatial and time scales.
Evolutionary biology; co-evolutions; genetics and evolution; branching processes and phyllotaxis.
Medical systems; physiology; cardiac modeling; computer models in Medicine; cancer research; epidemiology.
Numerical simulations and computations; numerical study and analysis of biological data.
Epistemology; history of science.
The journal will also publish book reviews.
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