论文标题
猎物proded剂系统中的自扩散驱动的模式形成，具有复杂栖息地的恐惧效果
Self-diffusion Driven Pattern Formation in Prey-Predator System with Complex Habitat under Fear Effect
论文作者
论文摘要
在目前的工作中，我们通过合并自我扩散来探讨栖息地复杂性对猎物和时空系统捕食者活动的影响。首先，我们通过纳入栖息地复杂性对猎物和捕食者功能反应的承载能力和恐惧效果的影响来修改Rosenzweig-Macarthur Predator-Prey模型。我们建立了非空间模型所有可行平衡点的存在和稳定性的条件，后来我们在分析和数值上证明了在不同的参数相平台中存在HopF和跨临界分叉的存在。研究了空间系统的稳定性，我们讨论了图灵不稳定性的条件。从图灵空间中选择合适的控制参数，使用振幅方程得出稳定图案的存在条件。从振幅方程的理论分析获得的结果是通过接近临界参数值的数值模拟结果来证明的。此外，根据数值模拟，我们说明了通过不同的模式形成在空间结构域中扩散的影响。因此，我们的模型清楚地表明，猎物和捕食者的功能反应的恐惧效果使抗侵犯行为包括栖息地复杂性，这有助于猎物通过扩散过程在时空领域生存。
In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by incorporating the effects of habitat complexity on the carrying capacity and fear effect of prey and predator functional response. We establish conditions for the existence and stability of all feasible equilibrium points of the non-spatial model and later we prove the existence of Hopf and transcritical bifurcations in different parametric phase-planes analytically and numerically. The stability of the spatial system is studied and we discuss the conditions for Turing instability. Selecting suitable control parameter from the Turing space, the existence conditions for stable patterns are derived using the amplitude equations. Results obtained from theoretical analysis of the amplitude equations are justified by numerical simulation results near the critical parameter value. Further, from numerical simulation, we illustrate the effect of diffusion of the dynamical system in the spatial domain by different pattern formations. Thus our model clearly shows that the fear effect of prey and predator's functional response make an anti-predator behaviour including habitat complexity which helps the prey to survive in the spatio-temporal domain through diffusive process.
