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Stochastic resonance and bifurcations in a harmonically driven tri-stable potential with colored noise
Yanxia Zhang1, Yanfei Jin1, Pengfei Xu1
1Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China.
Chaos (Woodbury, N.Y.)
|March 3, 2019
Summary
This study explores stochastic resonance (SR) and bifurcations in a tri-stable system. Optimal SR is achieved near stochastic bifurcations, enhancing performance in energy harvesting.
Area of Science:
- Nonlinear Dynamics
- Stochastic Systems Analysis
- Chaos Theory
Background:
- Stochastic resonance (SR) and stochastic bifurcations are critical phenomena in nonlinear systems.
- Understanding these phenomena is key to optimizing system performance, particularly in energy harvesting.
- Previous research has explored SR and bifurcations separately, but their interplay in tri-stable systems requires further investigation.
Purpose of the Study:
- To numerically investigate stochastic resonance (SR) and stochastic bifurcations in a nonlinear tri-stable system.
- To analyze the effects of system parameters on SR and bifurcations.
- To explore the relationship between SR and stochastic bifurcations and their application in energy harvesting.
Main Methods:
- Numerical simulations were employed to analyze a nonlinear tri-stable system subjected to colored noise and harmonic excitation.
- Key metrics including power spectral density, signal-to-noise ratio, stationary probability density (SPD), and largest Lyapunov exponent (LLE) were calculated.
- System parameters such as noise intensity, correlation time, well-depth ratio, and damping coefficient were systematically varied.
Main Results:
- Both noise-induced suppression and stochastic resonance (SR) were observed.
- Stochastic P-bifurcation was identified through changes in the stationary probability density (SPD) structure.
- Stochastic D-bifurcation was confirmed via the largest Lyapunov exponent (LLE) calculations.
- The optimal SR was found to occur near D-bifurcation, achievable with weak chaos.
Conclusions:
- The study demonstrates the occurrence of both P-bifurcation and D-bifurcation in the tri-stable system.
- A strong correlation between stochastic resonance and stochastic bifurcations was established.
- Exploiting SR and stochastic bifurcations can significantly improve the performance of tri-stable energy harvesters.
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