The Study Of Stochastic And Time Delay Effects In Active Brownian Particles

In this paper,the study of the dynamics of active Brownian particles?ABPs?is studied by stochastic and time delay theory in Schweizter-Ebeling-Tilch?SET?model.The study of active Brownian particles?ABPs?in SET model is added to time delay feedback in order to the research of the combinative effects of noise and time delay,and the study uses small time delay approximation theory in nonlinear system to obtain the stationary probability distribution?SPD??the mean first passage time?MFPT?and the signal-to-noise ratio?SNR?to study the transport property of active Brownian particles.The study briefly introduce the development history and research status of Brownian particles.The nonlinear dynamics related theories required in this thesis are summarized,including the derivation from the Langevin equation to the delayed Fokker-Planck equation,as well as the basic concepts of Gaussian white noise,correlated noise,and stochastic delay dynamics.Based on the basic theory of time,the expressions of physical quantities such as steady-state probability density,average first-pass time,and signal-to-noise ratio are obtained by using small time delay approximation theory to study the transport characteristics of active Brownian particles.The following results were obtained:The dynamical properties of active Brownian particles?ABPs?is investigated in the Schweitzer-Ebeling-Tilch?SET?model with time-delayed feedback,which is driven by external and internal noises.The effects of time-delayed feedback,external and internal noises on the stationary probability distribution?SPD?and the mean first passage time?MFPT?of the ABPs are discussed,respectively.The results are shown as following:?1?the intensity of delay feedback?K?can induce the phase transition between bimodal to unimodal states in the motion of a particle on the SPD;?2?the time delay can enhance the impacts of the intensity of delay feedback?K?thus it can induces transition from two stable states and?3?the MFPT as function of the noise strengths can be observed the maximum,which implies the signature of noise-enhanced stability?NES?phenomenon of the velocity in the ABPs for SET model.The positive or negative time delay feedback loop can enhance or weaken the stability of the motion of the ABPs.The stochastic resonance?SR?phenomenon of active Brownian particles is investigated in SET model with time delay feedback loop,we assume that the dynamics of ABPs is disturbed by both additive and multiplicative noise sources.The signal-to-noise ratio?SNR?is obtained to analyse the SR phenomenon.Our results shows that?1?the positive or negative time delay feedback?K?can enhance or weaken the stochastic resonance phenomenon;?2?the existence of a maximum and a minimum in the SNR as a function of extrinsic noise intensity ₁Q are identifying the characteristics of the SR phenomenon and stochastic reverse-resonance phenomenon,however for the curve of SNR as a function of intrinsic noise intensity ₂Q or cross-correlation intensity,there exhibits only a maximum;?3?the correlation intensity?can induce the stochastic reverse-resonance?SSR?phenomenon and reverse the impacts of the positive and negative time delay feedback loop in the SNR as a function of additive noise intensity Q₂;and?4?the time delay?can enhance the impacts of the intensity of delay feedback?K?.