Chaotic dynamics and subharmonic bifurcations of current‐carrying conductors subjected to harmonic excitation

Abstract

With both analytical and numerical methods, global dynamics including chaotic motions and subharmonic bifurcations of current‐carrying conductors subjected to harmonic excitation are investigated in this paper. The system parameter conditions for chaos are obtained with the Melnikov method. The monotonicity of the critical value for chaos on the damping, alternating current, and excitation amplitude is studied in detail for three cases. Some interesting dynamic phenomena such as “uncontrollable frequency interval” and “controllable frequency” are presented analytically. Subharmonic bifurcations of odd order or even order are also investigated with the subharmonic Melnikov method. The evolution of subharmonic bifurcation to chaos is studied. It is proved rigorously that the system may undergo chaotic motions through finite or infinite subharmonic bifurcations. Numerical simulations are given to verify the chaos threshold obtained with the analytical method.

Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

“…Kenmogne et al [35] analyzed the effects of the time-delay feedback position on the dynamical behavior of the nonlinear beam on elastic foundation, which is a fourth-order oscillator. Zhou et al [36] investigated global dynamics of current-carrying conductors subjected to harmonic excitation, which is a third-order oscillator. The system ( 7) is an oscillator with a sixth order potential, which is subjected to parameter excitation and square delayed feedback, and its analysis work is a challenge.…”

“…Zhou et al. [36] investigated global dynamics of current‐carrying conductors subjected to harmonic excitation, which is a third‐order oscillator. The system () is an oscillator with a sixth order potential, which is subjected to parameter excitation and square delayed feedback, and its analysis work is a challenge.…”