具有扩散和食饵趋向性的捕食者-食饵模型中的排斥趋化和捕食者逃避
Repulsive chemotaxis and predator evasion in predator prey models with diffusion and prey taxis
摘要：
研究了扩散型捕食模型中化学信号在捕食者逃逸中的作用，模型A考虑了捕食者的趋食性，模型B考虑了捕食者的趋食性，趋食性强度系数分别为$χ$和$ξ$.在模型的动力学部分，假设猎物的消耗率包括Holling，Bedington-DeAngelis或Crowley-Martin的功能反应。在空间维数n=1时，证明了模型A和模型B对任意$n\geq 1$都存在整体时间经典解. Crowley-Martin响应与信号产生的有界速率相结合，排除了$n\leq 3$模型A中解的爆破。研究了常微分方程和纯扩散模型稳定的常数共存定态的局部和全局稳定性，以及当$χ$超过某个临界值时模型B的Hopf分支机制.在模型A中，当$χ$和$ξ$足够大时，食饵的趋食性可能破坏共存稳态.数值模拟描述了两个模型的复杂时空模式的出现，并表明存在模型A的解，该解在有限时间内爆破$n=2$
英文摘要：
The role of predator evasion mediated by chemical signaling is studied in a diffusive prey-predator model when prey-taxis is taken into account (model A) or not (model B) with taxis strength coefficients $χ$ and $ξ$ respectively. In the kinetic part of the models it is assumed that the rate of prey consumption includes functional responses of Holling, Bedington-DeAngelis or Crowley-Martin. Existence of global-in-time classical solutions to model A is proved in space dimension n=1 while to model B for any $n\geq 1$. The Crowley-Martin response combined with bounded rate of signal production precludes blow-up of solution in model A for $n\leq 3$. Local and global stability of a constant coexistence steady state which is stable for ODE and purely diffusive model are studied along with mechanism of Hopf bifurcation for Model B when $χ$ exceeds some critical value. In model A it is shown that prey taxis may destabilize the coexistence steady state provided $χ$ and $ξ$ are big enough. Numerical simulation depicts emergence of complex space-time patterns for both models and indicate existence of solutions to model A which blow-up in finite time for $n=2$
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