Chaotic ferroresonance in a non-autonomous circuit

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 behavious 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 nth 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.