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Characterization in bi-parameter space of a non-ideal oscillator. (English) Zbl 1400.34060

Summary: 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 organized distribution of periodic windows, the ones known as Arnold tongues and also shrimp-shaped structures. In addition, we also identify intertwined basins of attraction for coexisting multiple attractors connected with tongues.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37B25 Stability of topological dynamical systems
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