Time-Periodic Perturbation Leading to Chaos in a Planar Memristor Oscillator Having a Bogdanov-Takens Bifurcation

Abstract

Memristor oscillators have been widely studied in the last years due to their potential applications in several technological areas. Electronic circuits containing a memristor are capable of producing nonlinear periodic and chaotic oscillations, due to their locally active characteristics. In this chapter, we consider a memristive circuit consisting of a locally active memristor, an inductor, and a resistor, which is modeled by a planar three-parameter system of ordinary differential equations. The system presents periodic oscillations, which arise at a Hopf bifurcation. We show that these oscillations evolve into a homoclinic orbit, in a Bogdanov-Takens-type bifurcation scenario. By adding a small time-periodic excitation to the circuit, we obtain complex dynamical behavior, such as quasiperiodic and chaotic oscillations. The system also presents multistability, having periodic oscillations coexisting with chaotic dynamics. As far as we know, it is the first time that time-periodic perturbation is used as the mechanism creation of chaotic dynamics in memristive systems.