The Mechanism Of Fractional Stochastic Resonance And Its Control By Applied Periodic Signal

Stochastic resonance (SR) is the phenomenon that the energy transferredfrom the noise signal to useful signal. But it will appear only when the weak periodicsignal, the noise signal and the system have the synergistic effect. Nowadays thereare so many research on SR of integer-order system which are applied to actualproduction process. This paper focused on the SR phenomenon and the controlmethod of fractional systems.There are a lot of anomalies in fractional-order system with respect to theinteger-order system, this paper used time memories of fractional-order systems.Combining the theory of fractional derivative, the Langevin equation can bederivated that is the foundation of fractional-order system simulation model.This paper used time domain and power spectral state of output response toanalyze the SR phenomenon of the system. By changing the fractional derivativeorder and noise intensity of the system, changes in the output response can beobserved. Then by analyzing the power spectrum of output response, the systemproducing the strength state of SR was studied.However in practical applications, the weak periodic signal of the system andthe noise signal are not changed, and its structural parameters is also fixed. It’sunrealistic to make the system produce SR phenomenon by changing the potentialbarrier height of the system. Using control methods of adding the external periodicsignal strengthenes or generates SR phenomenon purposefully, the output responsewith specific properties will occur, weak signal detection of the system will berealized.The paper also studied the control method of coupled two fractional ordersystems, the coupled systems coupled by two nonlinear fractional-order system isricher than a single fractional-order system dynamics. You can strengthen or produceSR of the under control system by changing the parameter of control system, thenyou can improve the quality of the output signal. The paper also studied the analog circuit implementing SR phenomenon offractional systems. First transfer the fractional operators to integer-order transferringfunction by using approximation method, and combine circuit design approach todesign analog circuit of the fractional system SR.That this paper studied fractional stochastic resonance phenomenon and itscontrol method for researching fractional system signal detection provides atheoretical foundation and research methods, which greatly accelerated the practicalapplication of fractional system SR methods.