鞍结分岔
数学
跨临界分岔
分岔图
倍周期分岔
分叉
分叉理论的生物学应用
李雅普诺夫指数
同宿分支
中央歧管
博格达诺夫-塔肯分岔
无限周期分岔
数学分析
分岔理论
控制理论(社会学)
应用数学
混乱的
霍普夫分叉
物理
非线性系统
计算机科学
控制(管理)
人工智能
量子力学
标识
DOI:10.1016/j.apm.2014.10.040
摘要
In this study, complex dynamics of a classical discrete-time predator–prey system are investigated. Rigorous results on the existence and stability of fixed points of this system are derived. It can also be shown that the system undergoes flip bifurcation, Neimark–Sacker bifurcation and codimension-two bifurcation associated with 1:2 resonance using the ideas of center manifold theorem, bifurcation theory and the normal form method. Specially, we give the explicit approximate expression of the invariant curve which is caused by the Neimark–Sacker bifurcation. At the same time, bifurcation phenomena and chaotic features are justified numerically via computing Lyapunov exponent spectrum. Results of numerical simulation verify our theoretical analysis. Finally, we extend the hybrid control strategy (state feed back and parameter perturbation) to control flip bifurcation and Neimark–Sacker bifurcation in two-dimensional discrete system.
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