Multistability and Jump in the Harmonically Excited SD Oscillator

Coexisting attractors and the consequent jump in a harmonically excited smooth and discontinuous (SD) oscillator with double potential wells are studied in detail herein. The intra-well periodic solutions in the vicinity of the nontrivial equilibria and the inter-well periodic solutions are generate...

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Bibliographic Details
Published in:Fractal and fractional 2023-04, Vol.7 (4), p.314
Main Authors: Wang, Zhenhua, Shang, Huilin
Format: Article
Language:English
Subjects:
Attractors (mathematics)
basin of attraction
Bifurcation theory
Energy
Equilibrium
fractal
hidden attractor
jump
multistability
Orbits
Oscillators
SD oscillator
Vibration
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Summary:Coexisting attractors and the consequent jump in a harmonically excited smooth and discontinuous (SD) oscillator with double potential wells are studied in detail herein. The intra-well periodic solutions in the vicinity of the nontrivial equilibria and the inter-well periodic solutions are generated theoretically. Then, their stability and conditions for local bifurcation are discussed. Furthermore, the point mapping method is utilized to depict the fractal basins of attraction of the attractors intuitively. Complex hidden attractors, such as period-3 responses and chaos, are found. It follows that jumps among multiple attractors can be easily triggered by an increase in the excitation level or a small disturbance of the initial condition. The results offer an opportunity for a more comprehensive understanding and better utilization of the multistability characteristics of the SD oscillator.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7040314