A predator-prey reaction-diffusion system with nonlocal effects
A predator-prey reaction-diffusion system with nonlocal effects
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DOI：
10.1007/bf00160498
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发表时间：
1996-02
影响因子：
1.9
通讯作者：
S. A. Gourley;N. Britton
中科院分区：
文献类型：
--
作者：
S. A. Gourley;N. Britton
考虑一个捕食-被捕食系统，它是一个具有积分项的反应扩散方程组，积分项代表被捕食者密度函数在过去时间和空间中的加权平均值.在极限情形下，系统退化为具有Logistic增长的Lotka沃尔泰拉扩散系统.我们研究了共存稳态的线性稳定性以及由此产生的分支，并构造了一些分支解的表达式。当非局部项实际上是局部项时，这些分叉都不会发生在退化情形中。
We consider a predator-prey system in the form of a coupled system of reaction-diffusion equations with an integral term representing a weighted average of the values of the prey density function, both in past time and space. In a limiting case the system reduces to the Lotka Volterra diffusion system with logistic growth of the prey. We investigate the linear stability of the coexistence steady state and bifurcations occurring from it, and expressions for some of the bifurcating solutions are constructed. None of these bifurcations can occur in the degenerate case when the nonlocal term is in fact local.