具有脉冲控制和病毒感染的害虫治理模型的分支分析

doi:10.6040/j.issn.1671-9352.2.2019.319

摘要/Abstract

摘要： 讨论了一类具有状态依赖反馈控制和病毒感染的害虫模型边界周期解的存在性, 得到了边界周期解全局稳定的条件。给出了模型发生跨临界分岔的条件,并通过数值方法分析了杀虫剂功效和单次投放感染害虫比例对实施控制措施的频率影响。研究结果说明,状态依赖控制措施在一定条件下可转化为周期控制措施;执行控制措施的频率随着单次投放感染害虫比例增大而减小, 但是随着杀虫剂功效增大,该频率可能减小也可能增大。

关键词: 害虫控制, 状态依赖反馈控制, 半动力系统, 周期解, 跨临界分支

Abstract: The existence of a boundary periodic solution is investigated for a pest management model with state-dependent feedback control and virus infection. The condition is derived for the global stability of the boundary periodic solution. It is examined how the transcritical bifurcation occurs for this model. It is addressed the impact of the control intensity, including the pesticide function and the releasing ratio of infected pests, on the frequency implementing the control measures. The main results obtained in this paper show that the state-dependent control policy can be converted into a periodic impulsive one. The frequency implementing control measures diminishes as the releasing ratio of infected pests increases; while it may decrease or increase as the pesticide function increases.

Key words: pest management, state-dependent feedback control, semi-dynamical system, periodic solution, transcritical bifurcation

中图分类号:

O175.7

王爱丽. 具有脉冲控制和病毒感染的害虫治理模型的分支分析[J]. 《山东大学学报(理学版)》, 2020, 55(7): 1-8.

WANG Ai-li. Transcritical bifurcation for a pest management model with impulse and virus infection[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(7): 1-8.

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