SPATIOTEMPORAL DYNAMICS OF TELEGRAPH REACTION-DIFFUSION PREDATOR-PREY MODELS
SPATIOTEMPORAL DYNAMICS OF TELEGRAPH REACTION-DIFFUSION PREDATOR-PREY MODELS
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DOI：
10.1142/9789814520829_0016
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
E. Hernandez‐Martinez;H. Puebla;Teresa Perez-Muñoz;M. González‐Brambila;J. Velasco-Hernández
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文献类型：
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作者：
E. Hernandez‐Martinez;H. Puebla;Teresa Perez-Muñoz;M. González‐Brambila;J. Velasco-Hernández
反应扩散（RD）方程是生态学中描述种群相互作用中传播效应的常用方程。基于Fick扩散方程，RD系统由抛物型偏微分方程（PDE）描述，因此涉及任意大种群速度。为了避免这种不切实际的情况下，我们引入Cattaneo的扩散在时空模型的捕食者相互作用，这导致更现实和有趣的种群之间的相互作用，可以是有用的，以获得见解的食物链动力学的理解。由此产生的模型就是所谓的电报RD模型。对具有Holling Ⅱ类功能反应和交叉扩散的捕食者-食饵模型进行了数值模拟，研究了弛豫时间对种群相互作用动力学的影响.
Reaction-diffusion (RD) equations are commonly used to describe the propagation effects in population interactions in ecology. RD system are described by parabolic partial differential equations (PDE), based on the Fick diffusion equation, hence arbitrary large population speeds are involved. To avoid this unrealistic situation, we introduce the Cattaneo’s diffusion in a spatiotemporal models of preypredator interactions, which leads to more realistic and interesting interactions between populations and can be useful to gain insights to the understanding of food-chain dynamics. The resulting model is the so-called telegraph RD model. Numerical simulations on predator-prey model with Holling type II functional response and cross-diffusion show the effects of the relaxation time in the dynamic of population interactions.