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

2015/07/24 by Sílvio L.T. de Souza, de Souza, S. L. T., Antônio M. Batista +7 · 1 citation
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1507.06791

openalex publication_date 2015/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Determining Lyapunov exponents from a time series

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