摘要
该文研究具有状态反馈脉冲控制的Holling-Tanner系统.在连续系统有唯一极限环及正平衡点为不稳定的焦点的前提下,利用微分方程几何理论、后继函数及数学分析的方法,获得脉冲系统阶1周期解的存在性、唯一性及轨道稳定性的充分条件.利用数值模拟验证主要结论,并且数值结果显示对某些参数在连续系统的极限环内存在脉冲系统的阶k周期解.
In this paper, we investigate the Holling-Tanner model with state feedback impulsive control. On the premise that the continuous system has a unique limit cycle and the positive equilibrium point is an unstable focus point, by means of the geometry theory of semicontinuous dynamic system, successor function method and mathematical analysis method, we obtain sufficient conditions for the existence, uniqueness and orbital stability of order 1 periodic solution of the impulsive system. The main conclusions are verified by numerical simulation. Moreover, the numerical results show that the impulsive system has order k periodic solutions within the limit cycle for some parameters.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2018年第1期174-189,共16页
Acta Mathematica Scientia
基金
国家自然科学基金(61364020)
玉林师范学院重点科研项目(2015YJZD02)~~
