Chaos, periodicity, and multistability in a plasma oscillator forced by a non-sinusoidal wave function

Abstract

In this paper we report on the dynamics of a plasma oscillator forced by a non-sinusoidal wave function, which is modeled by a six-parameter nonhomogeneous second-order ordinary differential equation. We keep four of these parameters constant, and investigate the dynamics of this system by varying other two parameters, namely $A$ and $\omega$, which are related to the amplitude and the angular frequency of the components of a Fourier series consisting of an expansion of cosine functions, that represents the external forcing. We investigate points in the two-dimensional $(\omega ,A)$ parameter-space of the forced plasma oscillator, with the dynamical behavior of each these points being characterized as regular or chaotic, depending on the magnitude of the largest Lyapunov exponent. Then we show that this parameter-space reveals regions of occurrence of the multistability phenomenon in the system. Properly generated bifurcation diagrams confirm this finding. Basins of attraction of coexisting periodic and chaotic attractors in the phase-space are presented, as well as the coexisting attractors themselves.