Effect of fear on two predator-one prey model in deterministic and fluctuating environment

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2021-03-22 DOI:10.5206/MASE/13541
D. Mukherjee
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引用次数: 2

Abstract

Recent ecological studies on predator-prey interactions has concentrated on determining the impacts of antipredator behavior due to fear of predators. These studies are mainly confined into one predator-one prey system. But in case of multiple predator attack on single prey species, fear mechanism is still unknown. The combined impact of multiple predator often cannot be anticipated from their independent effects. So coexistence of multiple predators and prey’s fitness becomes an important issue from an ecological point of view. Based on the above observations, we proposed and analyzed a model consisting of two competing predator sharing a common prey where prey’s reproduction rate is affected due to fear generated by the predators. We first study the boundedness, uniform persistence, stability and Hopf bifurcation of the deterministic model. Thereafter, we have investigated the existence and uniqueness of the global positive solution, boundedness, asymptotic stability of the stochastic model.  Numerical examples are provided to support our obtained  results.
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确定性和波动环境下恐惧对两捕食者-一猎物模型的影响
最近关于捕食者与猎物相互作用的生态学研究集中在确定由于对捕食者的恐惧而产生的反捕食者行为的影响上。这些研究主要局限于一个捕食者-一个猎物系统。但在多个捕食者攻击单个猎物的情况下,恐惧机制仍然未知。多个捕食者的联合影响往往无法从它们的独立影响中预测出来。因此,从生态学的角度来看,多种捕食者的共存和猎物的适应性成为一个重要问题。基于上述观察,我们提出并分析了一个由两个相互竞争的捕食者共享一个共同猎物组成的模型,其中捕食者产生的恐惧会影响猎物的繁殖率。我们首先研究了确定性模型的有界性、一致持久性、稳定性和Hopf分支。然后,我们研究了随机模型全局正解的存在唯一性、有界性和渐近稳定性。提供了数值例子来支持我们获得的结果。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
0
审稿时长
21 weeks
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