Global stability of single-species diffusion volterra models with continuous time delays
Global stability of single-species diffusion volterra models with continuous time delays
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DOI：
10.1007/bf02458861
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发表时间：
1987
影响因子：
3.5
通讯作者：
E. Beretta;Y. Takeuchi
中科院分区：
文献类型：
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作者：
E. Beretta;Y. Takeuchi
本文研究了具有连续时滞的单种群扩散连接斑块的稳定性，斑块内动力学为沃尔泰拉型.我们证明了该系统只能有两种平衡点：正平衡点和平凡平衡点。通过假设延迟核是适当的非负函数和归一化函数的凸组合，线性链技巧给出了O.D.E.具有与原始积分微分系统相同的稳定性。同伦函数技巧为正平衡点的存在性和全局稳定性提供了充分条件。我们还证明了任何正平衡点的局部稳定性以及正平衡点和平凡平衡点的局部不稳定性。所获得的结果的生物学意义进行了比较与已知的结果从文献中。
In this paper we consider the stability property of single-species patches connected by diffusion with a within-patch dynamics of Volterra type and with continuous time delays. We prove that this system can only have two kinds of equilibria: the positive and the trivial one. By the assumption that the delay kernels are convex combinations of suitable non-negative and normalized functions, the linear chain trick gives an expanded system of O.D.E. with the same stability properties as the original integro-differential system. Homotopy function techniques provide sufficient conditions for the existence of the positive equilibrium and for its global stability. We also prove the local stability of any positive equilibrium and the local instability both of positive and trivial equilibria. The biological meanings of the results obtained are compared with known results from the literature.