中国物理B ›› 2008, Vol. 17 ›› Issue (9): 3258-3263.doi: 10.1088/1674-1056/17/9/019

• GENERAL • 上一篇    下一篇

Chaotic ferroresonance in a non-autonomous circuit

惠萌, 张彦斌, 刘崇新   

  1. School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China
  • 收稿日期:2008-01-15 修回日期:2008-04-11 出版日期:2008-09-08 发布日期:2008-09-08
  • 基金资助:
    Project supported by the National High Technology Research and Development Program of China (Grant No 2006AA04Z180).

Chaotic ferroresonance in a non-autonomous circuit

Hui Meng(惠萌)†, Zhang Yan-Bin(张彦斌), and Liu Chong-Xin(刘崇新)   

  1. School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China
  • Received:2008-01-15 Revised:2008-04-11 Online:2008-09-08 Published:2008-09-08
  • Supported by:
    Project supported by the National High Technology Research and Development Program of China (Grant No 2006AA04Z180).

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摘要： Accurate description of magnetization curve has important effect on ferroresonance. In most of earlier ferroresonance studies the magnetization curve is modelled as a 3rd or 5th order polynomial. However, it is not comprehensive. This paper investigates the chaotic ferroresonance behaviour exhibited by a non-autonomous circuit which contains a nonlinear flux-controlled inductance. The ferromagnetic characteristic of this nonlinear inductance represented by a magnetization curve could be expressed as an $n$th order two-term polynomial. By varying the value of exponent $n$, the circuit can assume a diverse range of steady-state regimes including fundamental and subharmonic ferroresonance, quasi-periodic oscillations, and chaos. A detailed analysis of some simulations demonstrates that the probability of chaos increases as the exponent of the magnetization curve rises. The effect of varying the magnitude of the source voltage on the chaotic behaviour of the circuit is also studied.

Abstract: Accurate description of magnetization curve has important effect on ferroresonance. In most of earlier ferroresonance studies the magnetization curve is modelled as a 3rd or 5th order polynomial. However, it is not comprehensive. This paper investigates the chaotic ferroresonance behaviour exhibited by a non-autonomous circuit which contains a nonlinear flux-controlled inductance. The ferromagnetic characteristic of this nonlinear inductance represented by a magnetization curve could be expressed as an $n$th order two-term polynomial. By varying the value of exponent $n$, the circuit can assume a diverse range of steady-state regimes including fundamental and subharmonic ferroresonance, quasi-periodic oscillations, and chaos. A detailed analysis of some simulations demonstrates that the probability of chaos increases as the exponent of the magnetization curve rises. The effect of varying the magnitude of the source voltage on the chaotic behaviour of the circuit is also studied.

Key words: ferroresonance, chaotic behaviour, magnetization curve

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
75.60.Ej (Magnetization curves, hysteresis, Barkhausen and related effects) 84.30.Bv (Circuit theory)