中国物理B ›› 2012, Vol. 21 ›› Issue (10): 100501-100501.doi: 10.1088/1674-1056/21/10/100501

• GENERAL • 上一篇    下一篇

Dynamical behaviors of a system with switches between the Rössler oscillator and Chua circuits

张春, 余跃, 韩修静, 毕勤胜   

  1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
  • 收稿日期:2012-03-21 修回日期:2012-04-18 出版日期:2012-09-01 发布日期:2012-09-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 20976075).

Dynamical behaviors of a system with switches between the Rössler oscillator and Chua circuits

Zhang Chun (张春), Yu Yue (余跃), Han Xiu-Jing (韩修静), Bi Qin-Sheng (毕勤胜)   

  1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
  • Received:2012-03-21 Revised:2012-04-18 Online:2012-09-01 Published:2012-09-01
  • Contact: Bi Qin-Sheng E-mail:qbi@ujs.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 20976075).

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摘要： The behaviors of a system that alternates between the Rössler oscillator and Chua's circuit is investigated to explore the influence of the switches on the dynamical evolution. Switches related to the state variables are introduced, upon which a typical switching dynamical model is established. Bifurcation sets of the subsystems are derived via analysis of the related equilibrium points, which divide the parameters into several regions corresponding to different types of attractors. The dynamics behave typically in period orbits with the variation of the parameters. The focus/cycle periodic switching phenomenon is explored in detail to present the mechanism of the movement. The period-doubling bifurcation to chaos can be observed via the doubling increase of the turning points related to the switches. Furthermore, period-decreasing sequences have been obtained, which can be explained by the variation of the eigenvalues associated with the equilibrium points of the subsystems.

关键词: switching dynamical system, bifurcation mechanism, focus/cycle switching, chaotic oscillation

Abstract: The behaviors of a system that alternates between the Rössler oscillator and Chua's circuit is investigated to explore the influence of the switches on the dynamical evolution. Switches related to the state variables are introduced, upon which a typical switching dynamical model is established. Bifurcation sets of the subsystems are derived via analysis of the related equilibrium points, which divide the parameters into several regions corresponding to different types of attractors. The dynamics behave typically in period orbits with the variation of the parameters. The focus/cycle periodic switching phenomenon is explored in detail to present the mechanism of the movement. The period-doubling bifurcation to chaos can be observed via the doubling increase of the turning points related to the switches. Furthermore, period-decreasing sequences have been obtained, which can be explained by the variation of the eigenvalues associated with the equilibrium points of the subsystems.

Key words: switching dynamical system, bifurcation mechanism, focus/cycle switching, chaotic oscillation

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Pq (Numerical simulations of chaotic systems)