Stochastic Resonance Mechanism Of Some Fractional Order Stochastic Differential Equations

People have a bad impression on noise all the time,while what cannot be denied is that noise has played a significant role in various research fields.Based on this,Benzi proposed the term stochastic resonance,which has also attracted the extensive attention of a large number of researchers in many research fields.In this thesis,the stochastic resonance of three-dimensional fractional Langevin equation,Jerk oscillator with generalized MittagLeffler noise and two coupled fractional oscillators in Jerk equation are mainly studied.The following is the main contents:In Chapter 1,the problem background,research status at home and abroad,research content and innovation of this thesis are elaborated.Some definitions and formulas are briefly introduced,then some properties of Mittag-Leffler noise,dichotomous noise and trichotomous noise are summarized.In Chapter 2,the research on the stochastic resonance behavior of trapped particles described by three-dimensional fractional Langevin equation with multiplicative trichotomous noise is conducted.The generalized Shapiro-Loginov formula is adopted to derive the expressions of the first moment and output amplitude of the three-dimensional fractional Langevin equation,in which its stability and non-monotonicity of the image are discussed.The image is combined to explore and analyze the resonance phenomenon caused by trichotomous noise.In Chapter 3,the research on the resonance behavior of the Jerk oscillator affected by generalized Mittag-Leffler（GML）noise and multiplicative trichotomous noise is carried out.The analytical expressions of the first moment and the spectral amplification are derived.The graphical method is combined to discuss and analyze the resonance behavior of the Jerk oscillator.In Chapter 4,the resonance behavior of two coupled fractional harmonic oscillators under the influence of multiplicative dichotomous noise and external periodic force is considered based on the Jerk system.Based on the complete synchronization between the average behavior of the two oscillators,the Shapiro-Loginov formula is adopted to derive the accurate expressions of the first moment and the output amplitude gain.The image is combined to discuss and analyze the resonance behavior of the output amplitude gain.In Chapter 5,the important conclusions drawn in this thesis are summarized and the further prospects are illustrated.