具有强ALLEE效应的捕食者-猎物模型的双稳态和三稳态

IF 1.3 4区数学 Q3 BIOLOGY

Journal of Biological Systems Pub Date : 2023-02-09 DOI:10.1142/s0218339023500110

Ruma Kumbhakar, Saheb Pal, Nikhil Pal, Pankaj Tiwari

{"title":"具有强ALLEE效应的捕食者-猎物模型的双稳态和三稳态","authors":"Ruma Kumbhakar, Saheb Pal, Nikhil Pal, Pankaj Tiwari","doi":"10.1142/s0218339023500110","DOIUrl":null,"url":null,"abstract":"Understanding the Allee effect on endangered species is crucial for ecological conservation and management as it highly affects the extinction of a population. Due to several ecological mechanisms accounting for the Allee effect, it is necessary to study the dynamics of a predator–prey model incorporating this phenomenon. In 1999, Cosner et al. [Effects of spatial grouping on the functional response of predators, Theor Popul Biol 56:65–75, 1999] derived a new kind of functional response by considering spatially grouped predators. This paper deals with the dynamical behavior of a predator–prey system with functional response proposed by Cosner et al., and the growth of the prey population suffers a strong Allee effect. We find that the system undergoes various types of bifurcations such as Hopf bifurcation, saddle-node bifurcation, and Bogdanov–Takens bifurcation. We also observe that the model exhibits bistability and two different types of tristability phenomena. Our findings reveal that for such a kind of multistability in ecological systems, the initial population size plays a crucial role and also impacts the system’s state in the long term.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"BISTABILITY AND TRISTABILITY IN A PREDATOR–PREY MODEL WITH STRONG ALLEE EFFECT IN PREY\",\"authors\":\"Ruma Kumbhakar, Saheb Pal, Nikhil Pal, Pankaj Tiwari\",\"doi\":\"10.1142/s0218339023500110\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Understanding the Allee effect on endangered species is crucial for ecological conservation and management as it highly affects the extinction of a population. Due to several ecological mechanisms accounting for the Allee effect, it is necessary to study the dynamics of a predator–prey model incorporating this phenomenon. In 1999, Cosner et al. [Effects of spatial grouping on the functional response of predators, Theor Popul Biol 56:65–75, 1999] derived a new kind of functional response by considering spatially grouped predators. This paper deals with the dynamical behavior of a predator–prey system with functional response proposed by Cosner et al., and the growth of the prey population suffers a strong Allee effect. We find that the system undergoes various types of bifurcations such as Hopf bifurcation, saddle-node bifurcation, and Bogdanov–Takens bifurcation. We also observe that the model exhibits bistability and two different types of tristability phenomena. Our findings reveal that for such a kind of multistability in ecological systems, the initial population size plays a crucial role and also impacts the system’s state in the long term.\",\"PeriodicalId\":54872,\"journal\":{\"name\":\"Journal of Biological Systems\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-02-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Biological Systems\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218339023500110\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Biological Systems","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1142/s0218339023500110","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: 1

摘要

了解Allee对濒危物种的影响对生态保护和管理至关重要，因为它对种群的灭绝有很大影响。由于Allee效应的几种生态机制，有必要研究包含这一现象的捕食者-猎物模型的动力学。1999年，Cosner等人。[空间分组对捕食者功能反应的影响，Theor Popul Biol 56:65-751999]通过考虑空间分组的捕食者，得出了一种新的功能反应。本文研究了Cosner等人提出的具有功能响应的捕食者-被捕食系统的动力学行为。，并且猎物种群的增长受到强烈的Allee效应的影响。我们发现系统经历了各种类型的分叉，如Hopf分叉、鞍节点分叉和Bogdanov–Takens分叉。我们还观察到该模型表现出双稳态和两种不同类型的三稳态现象。我们的研究结果表明，对于生态系统中的这种多稳定性，初始种群规模起着至关重要的作用，也会影响系统的长期状态。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

BISTABILITY AND TRISTABILITY IN A PREDATOR–PREY MODEL WITH STRONG ALLEE EFFECT IN PREY

Understanding the Allee effect on endangered species is crucial for ecological conservation and management as it highly affects the extinction of a population. Due to several ecological mechanisms accounting for the Allee effect, it is necessary to study the dynamics of a predator–prey model incorporating this phenomenon. In 1999, Cosner et al. [Effects of spatial grouping on the functional response of predators, Theor Popul Biol 56:65–75, 1999] derived a new kind of functional response by considering spatially grouped predators. This paper deals with the dynamical behavior of a predator–prey system with functional response proposed by Cosner et al., and the growth of the prey population suffers a strong Allee effect. We find that the system undergoes various types of bifurcations such as Hopf bifurcation, saddle-node bifurcation, and Bogdanov–Takens bifurcation. We also observe that the model exhibits bistability and two different types of tristability phenomena. Our findings reveal that for such a kind of multistability in ecological systems, the initial population size plays a crucial role and also impacts the system’s state in the long term.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Biological Systems 生物-生物学

CiteScore

2.80

自引率

12.50%

发文量

审稿时长

1 months

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.