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Complicated behaviors as well as the mechanism of the switching circuit

Ma Xin-Dong Bi Qin-Sheng

Complicated behaviors as well as the mechanism of the switching circuit

Ma Xin-Dong, Bi Qin-Sheng
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  • Switching electrical circuit with switcher between different types of Jerk systems is established. Based upon the analysis of equilibrium states, stable focus as well as periodic oscillations via Hopf bifurcation can be observed in the two subsystems as parameters varies. Complicated behavior caused by the periodic switcher is investigated in detail, and the point/circle and circle/circle switching periodic oscillations as well as the mechanism are presented. In the different types of switching oscillations, the number of the switching points on the trajectory may increase doubly with the variation of the parameter, which may lead to the cascade of period-doubling bifurcation to chaos. Furthermore, the variation of the parameter may influence the amplitude of the periodic oscillation of the subsystem and therefore the structure of the attractor of the whole switching system.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 20976075, 10972091).
    [1]

    Zhusubaliyev Z H, Mosekilde E 2003 Bifurcation and Chaos in Piecewise-Smooth Dynamical Systems (Singapore: World Scientific )

    [2]

    Zhusubaliyev Z H, Mosekilde E 2008 Phys. Lett. A 372 2237

    [3]

    Baglietto M, Battistelli G, Scardovi L 2007 Automatica 43 1442

    [4]

    Cveticanin L, Abd El-Latif G M, El-Naggar A M, Ismail G M 2008 Journal of Sound and Vibration 318 580

    [5]

    Tousi M M, Karuei I, Hashtrudi-Zad S, Aghdam A G 2008 Systems, Control Letters 57 132

    [6]

    Santis E D, Benedetto M D D, Pola G 2008 Nonlinear Analysis: Hybrid Systems 2 750

    [7]

    Santis E D 2011 Systems, Control Letters 60 807

    [8]

    Xie G M, Wang L 2005 Journal of Computational and Applied Mathematics 181 176

    [9]

    Wu T Y, Zhang Z D, Bi Q S 2012 Acta Phys. Sin. 61 070502 (in Chinese) [吴天一, 张正娣, 毕勤胜 2012 物理学报 61 070502]

    [10]

    Sprott J C 2000 Phys. Lett. A 266 19

  • [1]

    Zhusubaliyev Z H, Mosekilde E 2003 Bifurcation and Chaos in Piecewise-Smooth Dynamical Systems (Singapore: World Scientific )

    [2]

    Zhusubaliyev Z H, Mosekilde E 2008 Phys. Lett. A 372 2237

    [3]

    Baglietto M, Battistelli G, Scardovi L 2007 Automatica 43 1442

    [4]

    Cveticanin L, Abd El-Latif G M, El-Naggar A M, Ismail G M 2008 Journal of Sound and Vibration 318 580

    [5]

    Tousi M M, Karuei I, Hashtrudi-Zad S, Aghdam A G 2008 Systems, Control Letters 57 132

    [6]

    Santis E D, Benedetto M D D, Pola G 2008 Nonlinear Analysis: Hybrid Systems 2 750

    [7]

    Santis E D 2011 Systems, Control Letters 60 807

    [8]

    Xie G M, Wang L 2005 Journal of Computational and Applied Mathematics 181 176

    [9]

    Wu T Y, Zhang Z D, Bi Q S 2012 Acta Phys. Sin. 61 070502 (in Chinese) [吴天一, 张正娣, 毕勤胜 2012 物理学报 61 070502]

    [10]

    Sprott J C 2000 Phys. Lett. A 266 19

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  • Received Date:  25 June 2012
  • Accepted Date:  11 July 2012
  • Published Online:  20 December 2012

Complicated behaviors as well as the mechanism of the switching circuit

  • 1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 20976075, 10972091).

Abstract: Switching electrical circuit with switcher between different types of Jerk systems is established. Based upon the analysis of equilibrium states, stable focus as well as periodic oscillations via Hopf bifurcation can be observed in the two subsystems as parameters varies. Complicated behavior caused by the periodic switcher is investigated in detail, and the point/circle and circle/circle switching periodic oscillations as well as the mechanism are presented. In the different types of switching oscillations, the number of the switching points on the trajectory may increase doubly with the variation of the parameter, which may lead to the cascade of period-doubling bifurcation to chaos. Furthermore, the variation of the parameter may influence the amplitude of the periodic oscillation of the subsystem and therefore the structure of the attractor of the whole switching system.

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