Transport Phenomena Driven By A Biharmonic Force And Resonance Phenomena In Local Potential

Based on the Langevin equation of the nonlinear dynamical system with non-Gaussian noise,by the approximate method and numerical simulation,transport phenomenon of Brownian particles driven by a biharmonic force and stochastic resonance in a confined asymmetrical bistable potential system are investigated.The influence of non-Gaussian noise and other parameters on the statistical properties of the system are discussed theoretically.Through theoretical analysis,some meaningful results are obtained,it provides a theoretical basis to explain the transport in biological processes and the realization of stochastic resonance in small-scale complex systems such as catalysis,biological channels and nano-materials.The main contents are as follows:On the one hand,we study the ratchet effect of an overdamped Brownian particle with a spatially symmetric potential driven by a biharmonic force under non-Gaussian noise.Based on second order Runge-Kutta algorithm,the average speed of Brownian particles is calculated.The ratcheting transport effect is discussed by the average velocity versus the non-Gaussian noise and the biharmonic force.It is found that the noise intensity D and the departure from the Gaussian noise q will suppress the ratchet transport effect,while the noise color will strengthen the ratchet transport effect.In addition,the phase differenceφ can destroy the symmetry of the overdamped Brownian system,and abundant transport phenomena are obtained duo to the destruction of the symmetry of the biharmonic force.At the same time,the phase difference φ mainly changes the transport direction.However,the amplitude of the biharmonic force η can change the waveform of the average velocity curve.It is worth noting that when the noise intensity is very small,the cooperation of the amplitude and phase of the biharmonic force can enrich the transport,and the biharmonic force has a greater influence on the transport phenomenon than the non-Gaussian noise.Hence,the transport effects presented in this paper may be helpful to explain the transport of a biological process and to understand theoretically the transport in 1D atom traps.On the other hand,the entropic stochastic resonance is discussed when an over-damped particles moving in a confined asymmetrical bistable potential driven by a weak signal and a non-Gaussian noise.The left potential of the bistable system can be adjusted by introducing the asymmetrical ratio a.By the functional analysis and two-state theory,the approximate Signal-to-Noise ratio(SNR)is derived.It is found that there is a global maximum in the SNR curves when the asymmetrical ratio a and the noise intensity D are changed.It is also shown that the noise correlation time τ will suppress the ESR of the system and the departure q can obviously change the position of peak in the SNR.The above clues are helpful in achieving weak signal detection under irregular,small-scale systems.