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周期切换下Rayleigh振子的振荡行为及机理
Oscillation b ehaviors and mechanism of Rayleigh oscillator with p erio dic switches
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摘要: 本文研究了自治与非自治电路系统在周期切换连接下的动力学行为及机理。基于自治子系统平衡点和极限环的相应稳定性分析和切换系统李雅普诺夫指数的理论推导及数值计算。讨论了两子系统在不同参数下的稳态解在周期切换连接下的复合系统的各种周期振荡行为，进而给出了切换系统随参数变化下的最大李雅普诺夫指数图及相应的分岔图，得到了切换系统在不同参数下呈现出周期振荡，概周期振荡和混沌振荡相互交替出现的复杂动力学行为并分析了其振荡机理。给出了切换系统通过倍周期分岔，鞍结分岔以及环面分岔到达混沌的不同动力学演化过程。Abstract: A system, which alternates between autonomous and non-autonomous circuit systems observing the time periodic switched rules, is investigated in order to explore its complicated dynamical behaviors. By analyzing the equilibrium point, limiting cycles, and the stability of the autonomous subsystems, as well as deriving the Lyapunov exponents of the switching systems in theory and numerical calculation, we have studied the variation of periodic oscillation behaviors of the compound systems with different stable solutions to the two subsystems. By using the bifurcation diagram of the switched systems and their corresponding largest Lyapunov exponent diagrams, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations and chaotic oscillations with different parameters in the switched systems. Furthermore, dynamical evolutions of the switching system to chaos by period-doubling bifurcations, saddle-node bifurcations and torus bifurcations are observed.
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