Sciences and Mathematics Faculty, College of Integrative Sciences and Arts, Arizona State University, Mesa, AZ 85212, United States. email:
Math Biosci Eng. 2017 Aug 1;14(4):843-880. doi: 10.3934/mbe.2017046.
Foraging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions. We provide completed local and global analysis of our model. Our analytical results combined with bifurcation diagrams suggest that: (1) dispersal may stabilize or destabilize the coupled system; (2) dispersal may generate multiple interior equilibria that lead to rich bistable dynamics or may destroy interior equilibria that lead to the extinction of predator in one patch or both patches; (3) Under certain conditions, the large dispersal can promote the permanence of the system. In addition, we compare the dynamics of our model to the classic two patch model to obtain a better understanding how different dispersal strategies may have different impacts on the dynamics and spatial patterns.
捕食者的觅食运动在猎物-捕食者系统的种群动态中起着重要作用，它们被认为是促进猎物和捕食者空间自组织的机制。在自然界中，有许多猎物-捕食者相互作用的例子，其中猎物是不动的，而捕食者通过不同的因素在斑块之间非随机地扩散，例如在遇到猎物后跟随刺激。在这项工作中，我们制定了一个只有捕食者具有流动性的 Rosenzweig-MacArthur 猎物-捕食者两斑块模型，并假设捕食者会向猎物-捕食者相互作用更集中的斑块移动。我们对我们的模型进行了完整的局部和全局分析。我们的分析结果与分岔图相结合表明：（1）扩散可能会稳定或破坏耦合系统；（2）扩散可能会产生多个内部平衡点，从而导致丰富的双稳态动力学，或者可能破坏内部平衡点，从而导致一个或两个斑块中的捕食者灭绝；（3）在某些条件下，大的扩散可以促进系统的持久性。此外，我们将我们的模型与经典的两斑块模型的动力学进行比较，以更好地理解不同的扩散策略如何对动力学和空间模式产生不同的影响。
