On almost periodicity of delayed predator-preymodel with mutual interference and discontinuous harvesting policies
On almost periodicity of delayed predator-preymodel with mutual interference and discontinuous harvesting policies
复制标题
具有相互干扰和不连续收获策略的延迟捕食者-被捕食者模型的几乎周期性
DOI：
10.1002/mma.3861
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发表时间：
2016
影响因子：
2.9
通讯作者：
Wang Dongshu
中科院分区：
文献类型：
--
作者：
Luo Daozhong;Wang Dongshu
本文的目的是研究一类具有相互干扰和贝丁顿-迪安吉利斯型功能响应的延迟捕食者-被捕食者模型的几乎周期性动力学，其中收获策略由不连续函数建模。基于泛函微分包含理论和集值分析，给出了具有不连续收获策略的系统Filippov意义解，并研究了系统Filippov意义正解的局部和全局存在性。通过采用广义微分不等式，可以获得一些有用的引理。然后，根据构造的引理，获得保证系统持久性的充分条件。通过构造一些合适的广义李雅普诺夫泛函，根据泛函微分包含理论和非光滑分析理论，导出了一系列关于系统几乎正周期解的存在性、唯一性和全局吸引力的有用判据。给出了一些合适的例子及其数值模拟来证实理论结果并说明系统的各种动态行为。版权所有 © 2016 约翰·威利父子有限公司
The objective of this paper is to investigate the almost periodic dynamics for a class of delayed predator–prey model with mutual interference and Beddington–DeAngelis type functional response, in which the harvesting policies are modeled by discontinuous functions. Based on the theory of functional differential inclusions theory and set‐valued analysis, the solution in sense of Filippov of system with the discontinuous harvesting policies is given, and the local and global existence of positive the solution in sense of Filippov of the system is studied. By employing generalized differential inequalities, some useful Lemmas are obtained. After that, sufficient conditions which guarantee the permanence of the system are obtained in view of the constructed Lemmas. By constructing some suitable generalized Lyapunov functional, a series of useful criteria on existence, uniqueness, and global attractivity of the almost positive periodic solution to the system are derived in view of functional differential inclusions theory and nonsmooth analysis theory. Some suitable examples together with their numeric simulations are given to substantiate the theoretical results and to illustrate various dynamical behaviors of the system. Copyright © 2016 John Wiley & Sons, Ltd.