Stochastic partial differential equation models for spatially dependent predator-prey equations
Stochastic partial differential equation models for spatially dependent predator-prey equations
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DOI：
10.3934/dcdsb.2019175
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
N. Nguyen;George Yin
中科院分区：
文献类型：
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作者：
N. Nguyen;George Yin
这项工作源于随机 Lotka-Volterra 或捕食者-猎物方程，旨在通过使用随机偏微分方程 (SPDE) 来模拟空间不均匀性。与经典模型相比，SPDE模型更加通用。为了纳入比率相关模型的更多定性特征，还使用了 Beddington-DeAngelis 函数响应。为了分析所考虑的系统，首先使用温和解的概念获得 SPDE 解的存在性和唯一性。然后导出持久和灭绝的充分条件。
Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more versatile. To incorporate more qualitative features of the ratio-dependent models, the Beddington-DeAngelis functional response is also used. To analyze the systems under consideration, first existence and uniqueness of solutions of the SPDEs are obtained using the notion of mild solution. Then sufficient conditions for permanence and extinction are derived.