Characterization in bi-parameter space of a non-ideal oscillator

Abstract

We investigate the dynamical behavior of a non-ideal Duffing oscillator, a system composed of a mass-spring-pendulum driven by a DC motor with limited power supply. To identify new features on Duffing oscillator parameter space due to the limited power supply, we provide an extensive numerical characterization in the bi-parameter space by using Lyapunov exponents. Following this procedure, we identify remarkable new periodic windows, the ones known as Arnold tongues and also shrimp-shaped structures. Such windows appear in highly organized distribution with typical self-similar structures for the shrimps, and, surprisingly, codimension-2 bifurcation as a point of accumulations for the tongues.