A Lotka-Volterra system with patch structure (related to a multi-group SI epidemic model)
A Lotka-Volterra system with patch structure (related to a multi-group SI epidemic model)
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DOI：
10.3934/dcdss.2015.8.999
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发表时间：
2015-07
期刊：
影响因子：
--
通讯作者：
Y. Muroya
中科院分区：
文献类型：
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作者：
Y. Muroya
本文针对与多群 SI 流行病模型相关的具有无限时滞和斑块结构的 Lotka-Volterra 系统，应用 Lyapunov 函数技术，不使用瞬时负项对无限时滞项的对角优势形式，通过阈值参数 $s(M(0))$ 建立完整的全局动力学，即，如果 $s(M(0)) \leq 0$ 则平凡均衡全局渐近稳定，并且全局正均衡全局如果 $s(M(0))>0$ 则渐近稳定。这为具有补丁结构的Lotka-Volterra系统提供了新型的全局稳定性条件。
In this paper, for a Lotka-Volterra system with infinite delays and patch structure related to a multi-group SI epidemic model, applying Lyapunov functional techniques without using the form of diagonal dominance of the instantaneous negative terms over the infinite delay terms, we establish the complete global dynamics by a threshold parameter $s(M(0))$, that is, the trivial equilibrium is globally asymptotically stable if $s(M(0)) \leq 0$ and the positive equilibrium is globally asymptotically stable if $s(M(0))>0$, respectively. This offer new type condition of global stability for Lotka-Volterra systems with patch structure.