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A stochastic averaging technique based on energy-dependent frequency isextended to dynamical systems with triple-well potential driven by colorednoise. The key procedure is the derivation of energy-dependent frequencyaccording to the four different motion patterns in triple-well potential.Combined with the stochastic averaging of energy envelope, the analyticalstationary probability density (SPD) of tri-stable systems can be obtained. Twocases of strongly nonlinear triple-well potential systems are presented toexplore the effects of colored noise and validate the effectiveness of theproposed method. Results show that the proposed method is well verified bynumerical simulations, and has significant advantages, such as high accuracy,small limitation and easy application in multi-stable systems, compared withthe traditional stochastic averaging method. Colored noise plays a significantconstructive role in modulating transition strength, stochastic fluctuationrange and symmetry of triple-well potential. While, the additive andmultiplicative colored noises display quite different effects on the featuresof coherence resonance (CR). Choosing a moderate additive noise intensity caninduce CR, but the multiplicative colored noise cannot.

Stochastic dynamics of the triple-well potential systems driven by colored noise