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Stability switching and chaos in a multiple delayed prey-predator model with fear effect and anti-predator behavior

机译:具有恐惧效应和反捕食性行为的多延迟猎物捕食者模型中的稳定性切换和混沌

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Recent studies demonstrate that the density of prey population is not only affected by direct killing by the predator, but the fear in prey caused by predator also reduces it by cutting down the reproduction rate of prey community, and prey shows anti-predator behavior in response to this fear. In this study, we propose a prey-predator model with fear in prey due to predator and anti-predator behavior by prey against the predator with fear response delay and gestation delay. It is assumed that the predator consumes prey via simplified Holling Type-Ⅳ functional response. We evaluate the equilibrium points and study the local and global stability behavior of the system around them. It is observed that our system undergoes Hopf-bifurcation with respect to the fear parameter. Moreover, the system shows the attribute of bi-stability involving two stable equilibriums. Further, we study the dynamics of the delayed system by incorporating fear response delay and gestation delay. We observe that the delayed system suffers Hopf-bifurcation with respect to both delays. Using the normal form method and center manifold theory, the direction and stability of Hopf-bifurcation are studied. Chaotic behavior for delayed system is observed for large values of fear response delay. All these findings are supported by numerical simulation.
机译:最近的研究表明,捕食者的猎物密度不仅受到捕食者直接杀害的影响,而捕食者引起的猎物恐惧也通过减少猎物社区的再现率来减少它,并且猎物表明反捕食者行为是响应的抗捕食者行为对此恐惧。在这项研究中,我们提出了一种捕食者模型,由于捕食者和抗捕食者行为,以捕食者对捕食者的捕食者行为具有恐惧响应延迟和妊娠延迟。假设捕食者通过简化的Holling型ⅳ功能响应消耗猎物。我们评估均衡点并研究它们周围系统的本地和全球稳定行为。观察到我们的系统对恐惧参数进行了跳跃分叉。此外,该系统显示了涉及两个稳定平衡的双稳定性的属性。此外,我们通过纳入恐惧响应延迟和妊娠延迟来研究延迟系统的动态。我们观察到延迟系统对两次延迟遭受跳跃分叉。使用正常形式的方法和中心歧管理论,研究了Hopf-Bifurcation的方向和稳定性。观察到延迟系统的混沌行为对于恐惧响应延迟的大值。所有这些发现都得到了数值模拟的支持。

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