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.


34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37B25 Stability of topological dynamical systems
Full Text: DOI arXiv


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