Study On Vibrational Resonance Of Bistable System Driven By Multiplicative Signals

This paper studies the vibration resonance induced by multiplicative signals.Using the method of separation of fast and slow variables,we use the form of dynamic equations to decompose the kinetic equation into two parts.After a series of derivation,we finally obtain the linear response function of the bistable system to low-frequency signals under the action of multiplicative signals.And the analytical expression of the nonlinear response function.The results show that the multiplicative signal,like the additive signal,can induce the vibrational resonance behavior of the system,and this behavior depends on the frequency of the high frequency signal and the amplitude and frequency of the low frequency signal.The phenomenon of multiplicative vibration resonance between the first harmonic and the second harmonic is distinctly different.Under the driving of multiplicative signals,the system has a phase transition from bistable to monostable.The induced vibration resonance phenomenon exists in the linear region.It also exists in the non-linear region.The innovation of this dissertation is to use the effect of multiplicative signals instead of the additive signal used in the past.In terms of theoretical research value,the introduction of multiplicative signals is a useful complement to the field of vibration resonance.In practical applications,the strange phenomenon of vibration resonance has broad application prospects in vertical cavity surface emitting lasers,etc.The introduction of research provides a theoretical basis for more experimental research,provides possibilities for the realization of more experiments,and exerts its potential role in multiple scientific and technological fields.