Dynamical behavior analysis and bifurcation mechanism of a new 3-D nonlinear periodic switching system
Dynamical behavior analysis and bifurcation mechanism of a new 3-D nonlinear periodic switching system
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DOI：
10.1007/s11071-013-0910-z
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发表时间：
2013-05
影响因子：
5.6
通讯作者：
Yue Yu;Chun Zhang;Xiujing Han;Qinsheng Bi
中科院分区：
文献类型：
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作者：
Yue Yu;Chun Zhang;Xiujing Han;Qinsheng Bi
提出了一个新的周期切换混沌系统，它与原有的单一混沌系统拓扑不等价。特别值得注意的是，周期切换混沌系统可以在很宽的参数域中产生稳定的解，并具有丰富的动力学现象。通过适当选择参数，研究了稳定极限环的存在性。讨论了由Rössler系统和蔡氏电路组成的等周期切换系统的复杂动力学演化。进而得到了系统在切换边界处可能的分岔行为。对系统不同行为的机理进行了探讨。指出系统的轨迹存在明显的切换点，这些切换点是由周期信号决定的。同时，系统可能通过倍周期分岔而进入混沌，导致轨迹与非光滑边界点之间的切换碰撞。通过理论分析和数值仿真研究了该系统的复杂动力学问题。此外，还讨论了这种周期切换系统的控制方法。我们得到的结果清楚地表明，非线性开关系统包括不同的波形和频率，它值得更详细的研究。
This paper presents a new periodic switching chaotic system, which is topologically non-equivalent to the original sole chaotic systems. Of particular interest is that the periodic switching chaotic system can generate stable solution in a very wide parameter domain and has rich dynamic phenomena. The existence of a stable limit cycle with a suitable choice of the parameters is investigated. The complex dynamical evolutions of the switching system composed of the Rössler system and the Chua’s circuit are discussed, which is switched by equal period. Then the possible bifurcation behaviors of the system at the switching boundary are obtained. The mechanism of the different behaviors of the system is investigated. It is pointed out that the trajectories of the system have obvious switching points, which are decided by the periodic signal. Meanwhile, the system may be led to chaos via a period-doubling bifurcation, resulting in the switching collisions between the trajectories and the non-smooth boundary points. The complicated dynamics are studied by virtue of theoretical analysis and numerical simulation. Furthermore, the control methods of this periodic switching system are discussed. The results we have obtained clearly show that the nonlinear switching system includes different waveforms and frequencies and it deserves more detailed research.