Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property
Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property
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双稳态藻鱼系统脉冲状态反馈控制的定性分析
DOI：
10.1016/j.amc.2015.09.046
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发表时间：
2015
影响因子：
4
通讯作者：
Xinyu Song
中科院分区：
文献类型：
--
作者：
Hongjian Guo;Lansun Chen;Xinyu Song
提出了一种消费者-资源系统来描述富营养化水体中藻类和鱼类的双向相互作用。所提出的连续系统的动力学特性。在此情况下，建立了一个依赖于藻类生物量的脉冲半离散系统，并研究了状态反馈控制的可行性，以维持两种藻类的共存.脉冲半连续系统有三种情况，分别对应于三种控制措施：放鱼、喷洒灭藻剂、放鱼与喷洒灭藻相结合的综合控制。利用后继函数分别讨论了三个模型一阶周期解的存在性。利用Poincaré映射和Poincaré判据的类比，给出了一阶周期解稳定的条件.数学结果表明，对于三种控制策略中的每一种，都存在一个控制参数范围，在这个范围内，相应的控制是可行的。最后通过数值仿真验证了这些数学结果，并给出了实际意义.
A kind of consumer-resource system is proposed to describe the bidirectional interactions of the algae and the fish in an eutrophic water body. The dynamical properties of the proposed continuous system are given. For the bistable case, an impulsive semidynamical system with state feedback control, which depends on the biomass of the algae, is formulated and investigated to consider the feasibility of state feedback control for the aim of maintaining two species coexisting. The impulsive semidynamical system has three cases corresponding to three kinds of control measures: releasing fish, spraying algaecide, integrated control combining releasing fish and spraying algaecide. The existences of order-1 periodic solutions of three models are discussed by using successor function, respectively. The conditions under which the order-1 periodic solution is stable are given by using the Poincaré map and the analogue of Poincaré criterion. Mathematical results show that, for every one of three control strategies, there exists a range of control parameter in which the corresponding control is feasible. Finally, those mathematical results are verified by numerical simulations and the practical meanings are given.