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arXiv · 1904.02908

Multi-stability in Doubochinski's Pendulum

Yao Luo·Wenkai Fan·Chenghao Feng·Sihui Wang·Yinlong Wang
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Abstract

The widespread phenomena of multistability is a problem involving rich dynamics to be explored. In this paper, we study the multistability of a generalized nonlinear forcing oscillator excited by $f(x)cos ωt$. We take Doubochinski's Pendulum as an example. The so-called "amplitude quantization", i.e., the multiple discrete periodical solutions, is identified as self-adaptive subharmonic resonance in response to nonlinear feeding. The subharmonic resonance frequency is found related to the symmetry of the driving force: odd subharmonic resonance occurs under even symmetric driving force and vice versa. We solve the multiple periodical solutions and investigate the transition and competition between these multi-stable modes via frequency response curves and Poincare maps. We find the irreversible transition between the multistable modes and propose a multistability control strategy.

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Yao Luo, Wenkai Fan, Chenghao Feng, Sihui Wang, Yinlong Wang. 2019-04-05. Multi-stability in Doubochinski's Pendulum. https://arxiv.org/abs/1904.02908

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