Multistability, period-adding, and fractality in a plasma oscillator

Abstract

In this paper, we report on a periodically driven plasma oscillator modeled by a six-parameter nonhomogeneous second-order ordinary differential equation. We fix four of these parameters, and investigate the dynamics of this system by varying the other two, namely, the amplitude A and the angular frequency ω of the driving. In other words, we investigate the (ω,A) parameter plane, where the dynamical behavior of each point was characterized by the magnitude of the largest Lyapunov exponent. Then, we show that this parameter plane reveals the 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. We also report on the organization of periodicity and chaos in the (ω,A) parameter plane. Typical periodic structures were detected embedded in a chaotic region, namely, the cuspidal, the non-cuspidal, and the shrimp-like. At a certain location on the parameter plane, the organization of the shrimp-like periodic structures resembles a fractal, since the same shape is seen when we look through different scales. Elsewhere these same structures appear organized in a period-adding sequence.