The Stochastic Resonance In A Class Of Coupled Systems Excited By Stochastic Noise

Stochastic resonance refers to the synergistic effect of nonlinear systems under the combined action of noise and signal.Specifically,when the noise,signal and system parameters reach the best matching degree,the signal-to-noise ratio of the system output increases.In recent years,stochastic resonance theory has gradually matured and is widely used in various scientific fields.With the increasing complexity and relevance of research models,high-dimensional models are closer to reality and can better reflect the essence of things.Therefore,this paper studies stochastic resonance based on a class of coupled network systems.Firstly,we studied is the synergistic effect of asymmetric bistable coupled network systems under the action of Gaussian colored noise and periodic signal.The system is a network model consisting of a large number of oscillators.The interaction and change between individuals produce complex nonlinear behavior patterns.For further research,the original N-dimensional system is reduced and approximated by using the mean field theory,the unified colored noise approximation theory and the equivalent nonlinearization method;Secondly,the Langevin equation of simplified model is obtained through the slaving principle,using the two-state model theory derives the theoretical expression of signal-to-noise ratio.It is found that the system produces the phenomenon of scale stochastic resonance.At the same time,the effects of Gaussian color noise parameters,system parameters and periodic signal parameters on the stochastic resonance behavior of asymmetric coupled network systems are discussed.The results show that the increase of Gaussian color noise parameters can promote stochastic resonance phenomenon.And the stochastic resonance phenomenon of the system driven by the Gaussian colored noise and the Gaussian white noise,respectively,are analyzed and compared with each other.Research result shows that Gaussian colored noise is more conducive to enhancing stochastic resonance phenomenon.Secondly,we discussed the stochastic resonance behavior of time-delayed bistable coupled network systems under the action of Gaussian white noise and periodic signal.The original system is reduced and approximated by using the mean field theory and the small delay approximation method,and the simplified model is obtained.The analytical expressions of signal-to-noise ratio is derived in the adiabatic limit.Based on this,it is found that the coupled system produces stochastic resonance.Then,the effect of system scale on time-delayed coupled systems is discussed.It is found that when the system scale increases to a certain extent,the signal-to-noise ratio curve evolves from single peak to double peak,that is,double stochastic resonance occurs in the system.And,the effects of time delay,system parameters and periodic signal parameters on the stochastic resonance and double stochastic resonance behavior of the system are analyzed respectively.It is found that the effect of time delay on the system depends on the positive or negative of the time delay feedback strength.The influence of time delay on the double stochastic resonance of this system is weaker than that of single stochastic resonance.In single stochastic resonance,as the coupling coefficient increases,the output effect of the system first increases and then decreases.However,in the double stochastic resonance,the output response of the system decreases with the increase of the coupling coefficient.Finally,based on the research of symmetric time-delayed bistable coupled system,analyzes the stochastic resonance phenomenon of asymmetric time-delayed bistable coupled system driven by Gaussian white noise.According to the expression of signal-to-noise ratio,the effects of the parameters such as asymmetric coefficient,noise intensity and time delay feedback strength on the stochastic resonance are discussed in detail.The results show that larger asymmetric parameters and noise intensity can enhance the occurrence of stochastic resonance behavior.On the contrary,increasing the time delay feedback strength suppresses stochastic resonance of the system.