Multistability and organization of chaos and quasiperiodicity in a memristor-based Shimizu-Morioka oscillator under two-frequency excitation

In this paper we investigate the organization of chaos and quasiperiodicity in a parameter plane of a continuous-time three-dimensional nonautonomous dynamical system. More specifically, we investigate a memristor-based Shimizu-Morioka oscillator, where the external excitation is represented by the sum of two different sinusoidal functions with angular frequencies ω1 and ω2. Through a scan carried out in the (ω1, ω2) parameter plane, with the dynamical behavior of each point in the phase-space being characterized by the Lyapunov exponents spectrum, we show that this system presents chaos and quasiperiodicity regions, without presenting, however, periodicity regions. Parameter regions for which the multistability phenomenon was detected, also are observed. Basins of attraction of coexisting chaotic and quasiperiodic attractors, as well as the attractors themselves, are reported.