{"title":"A delay non-autonomous model for the combined effects of fear, prey refuge and additional food for predator.","authors":"Nazmul Sk, Pankaj Kumar Tiwari, Samares Pal, Maia Martcheva","doi":"10.1080/17513758.2021.2001583","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we investigate the combined effects of fear, prey refuge and additional food for predator in a predator-prey system with Beddington type functional response. We observe oscillatory behaviour of the system in the absence of fear, refuge and additional food whereas the system shows stable dynamics if anyone of these three factors is introduced. After analysing the behaviour of system with fear, refuge and additional food, we find that the system destabilizes due to fear factor whereas refuge and additional food stabilize the system by killing persistent oscillations. We extend our model by considering the fact that after sensing the chemical/vocal cue, prey takes some time for assessing the predation risk. The delayed system shows chaotic dynamics through multiple stability switches for increasing values of time delay. Moreover, we see the impact of seasonal change in the level of fear on the delayed as well as non-delayed system.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"15 1","pages":"580-622"},"PeriodicalIF":1.8000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Biological Dynamics","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1080/17513758.2021.2001583","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECOLOGY","Score":null,"Total":0}
引用次数: 5
Abstract
In this paper, we investigate the combined effects of fear, prey refuge and additional food for predator in a predator-prey system with Beddington type functional response. We observe oscillatory behaviour of the system in the absence of fear, refuge and additional food whereas the system shows stable dynamics if anyone of these three factors is introduced. After analysing the behaviour of system with fear, refuge and additional food, we find that the system destabilizes due to fear factor whereas refuge and additional food stabilize the system by killing persistent oscillations. We extend our model by considering the fact that after sensing the chemical/vocal cue, prey takes some time for assessing the predation risk. The delayed system shows chaotic dynamics through multiple stability switches for increasing values of time delay. Moreover, we see the impact of seasonal change in the level of fear on the delayed as well as non-delayed system.
期刊介绍：
Journal of Biological Dynamics, an open access journal, publishes state of the art papers dealing with the analysis of dynamic models that arise from biological processes. The Journal focuses on dynamic phenomena at scales ranging from the level of individual organisms to that of populations, communities, and ecosystems in the fields of ecology and evolutionary biology, population dynamics, epidemiology, immunology, neuroscience, environmental science, and animal behavior. Papers in other areas are acceptable at the editors’ discretion. In addition to papers that analyze original mathematical models and develop new theories and analytic methods, the Journal welcomes papers that connect mathematical modeling and analysis to experimental and observational data. The Journal also publishes short notes, expository and review articles, book reviews and a section on open problems.
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