Study On Coupled Fractional Brownian Motors With Stochastic Interactions

As an important research frontier of nonlinear science and modern statistical physics,the study of various positive effects of random force on macroscopic systems under nonlinear condition,has universal significance and practical value for the practical application of random force in physical,chemical,biological and engineering systems.In particular,with the rapid development of fractional calculus,fractional stochastic dynamical system has received widespread attention for the practical problems of viscoelastic material,fractal medium,chaotic background,anomalous diffusion,etc.Fractional stochastic differential equation can provide a more accurate mathematical description of many practical problems in physics,biology,chemistry and engineering,therefore,it has attracted extensive attention.At the same time,the directed transport phenomenon of molecular motor is one of the most striking problem in molecular biology,physics and biochemistry,and the stochastic resonance phenomenon is ubiquitious in many different fields,which are attracting more and more attention in recent years.However,so far,the traditional studies of the two phenomena mentioned above are mostly based on the integer stochastic differential equations.More and more experiments show that the fractional stochastic differential equations can simulate more accurately the transport phenomenon of molecular motor in cytosol,because of the time memory and the long-rang spatial correlation of fractional calculus.It is a very meaningful work to study the transport phenomenon of molecular motor and the stochastic resonance phenomenon of linear oscillator by using fractional stochastic differential equation.But in some physical or biological environments,where the surrounding medium contains many particles of the same kind as coupled Brownian particles,and they are capable of not only decoupling from the original coupled system,but also adhering to each other,and recoupling a larger system.Thus two mathematical models are proposed based on Langevin equations(LEs)to characterize the random interactions with fluctuating number of Brownian particles in the stochastic coupled system.The first one is proposed to characterize the fluctuation on head and tail of the chain of the coupled system,the second one is proposed to characterize the random interactions with fluctuating number of Brownian particles in the centralized coupled system.By the system simulations,the effects of interacting parameters,ratchet asymmetry and noisy intensity,on collective transport behaviors,are investigated,and some phenomena,such as cooperative behaviors,stochastic resonance(SR)and generalized SR,are observed.