多涡卷振荡体系的复杂动力学行为及控制

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摘要通过电压控制电流型分段线性电阻NR的伏安特性引入非光滑因素，调节电路中可调电子元器件，使得系统参数之间表现出巨大差异从而构建一个具有两尺度效应的四维非光滑快慢耦合簇发振荡电路系统。为了分析快变系统在各个分界面的平衡态及稳定性和系统轨迹在穿越非光滑分界面时产生的簇发机制，选取两组不同参数，理论分析结合数值仿真，揭示了快变系统在穿越非光滑分界面时不同簇发现象的产生机制和非光滑分岔对簇发机制的影响。最后，利用R-L型分数阶微积分算子对两尺度快慢耦合簇发电路系统进行分数阶转换并对该分数阶电路系统进行了单涡卷，双涡卷，三涡卷及四涡卷混沌的控制。

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	张艳龙1
	崇富权1
	王丽2
	苏程1

关键词 ：两尺度法, 非光滑分岔, 簇发机制, 分数阶控制

Abstract：The non-smooth factor was introduced into the volt-ampere characteristics of the voltage-controlled current-mode segment linear resistor to adjust the adjustable electronic components in the circuit. It makes a great difference between the system parameters and constructs a four-dimensional non-smooth fast-slow coupling cluster oscillation circuit system with two-scale effect. In order to analyze the equilibrium state and stability of the fast-varying system at each interface and the clustering mechanism of the system trajectory passing through the non-smooth interface, two sets of different parameters were selected, theoretical analysis and numerical simulation were combiled. The occurrence mechanism of different clustering phenomena and the influence of non-smooth bifurcation on the clustering mechanism when fast-varying systems crossing non-smooth interfaces were revealed. Finally, the fractional transformation of the two-scale fast-slow coupling cluster circuit system was carried out by using the R-L fractional calculus operator, and the single-scroll, double-scroll, three-scroll and four-scroll chaotic control of the fractional circuit system is carried out.

Key words： Two-scale method Non-smooth bifurcation Clustering mechanism Fractional control

收稿日期: 2018-05-28 出版日期: 2020-03-28

引用本文:

张艳龙1，崇富权1，王丽2，苏程1. 多涡卷振荡体系的复杂动力学行为及控制[J]. 振动与冲击, 2020, 39(7): 268-274.
ZHANG Yanlong1， CHONG Fuquan1， WANG Li2， SU Cheng1. Complex dynamic behavior and control of a multi-scroll oscillation system. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(7): 268-274.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I7/268

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