| This dissertation studies the regulation of periodic force on stochastic systems.First,the research status and research significance of periodic force for stochastic system are reviewed.Secondly,a comprehensive introduction is given to the research method of stochastic dynamical system under cyclic force.Next,we study the effect of periodic force on the dynamic behavior of inertial Brown motor.Finally,we study the effect of periodic force on the metastable stability of Logistic system.In the part of "the study of the effect of periodic force on the dynamic behavior of the inertial Brown motor",the negative transfer phenomenon at relatively high temperature is observed in the inertial Brown motor through the oscillating signals of two harmonic components.For the same system driven by monochromatic signals,negative transfer(either from thermal wave or coexistence attractor)can not exist,at high temperature.The existence of double harmonics improves the temperature range of observation of abnormal transport behavior.The result may provide an alternative to control the abnormal transport of the inertial Brown motor.The inertial Brown motor under the influence of biasing double harmonic signals is studied numerically.For the limited positive partial pressure,the maximum negative current occurs at a relatively large noise intensity,and the size of the abnormal velocity is also very large.The results mean that a significantly abnormal transport,behavior can be observed at relatively high temperatures by a dual tuned drive.This chapter mainly considers the abnormal mobility of Brown motor under the control of harmonic mixing.The results show that this is an effective control method,and it can also meet the two goals of higher temperature existence and larger magnitude of counter direction transport,which is helpful for further experimental research.Because of the appearance of the relative phase shift,the double harmonic signal leads to the symmetry breaking of the time inversion,so that the particle has the "ability" to resist the external force.When an extra time period signal plays the role of noise in Brown motor,an anomalous transport phenomenon can be observed in the corresponding vibration motor:absolute negative mobility.In the appropriate parameter area,there are two optimal regions for the absolute negative transfer rate behavior with the increase of bias.The absolute negative transfer rate can exist for the amplitude and frequency of the signal in a large range.In the parameter region of deterministic attractor control,by controlling the amplitude of the additional periodic signal,We can observe some interesting phenomena.Such as,the absolute negative transfer rate,the nonlinear negative transfer rate and the difference negative transfer rate.These phenomena can be explained by the coexistence attractor theory.In this chapter,we study how the harmonic mixing method is used to control the anomalous transport behavior in the inertial Brown motor.When the control system is transported by harmonic mixing,we can observe strong backward direction transport at higher temperature,which has a good theoretical guidance for the experimental research.The effect of periodic force on the stability of metastable state of Logistic model is studied,we investigate the effect of periodic force on the steady state stability of Logistic model.The mean first pass time(MFPT)of the system is derived from metastable state to steady state.Based on the expression,the influence of periodic force on the mean first pass time(MFPT)is analyzed.The results are as follows:1.the multiplicative noise induced transitions,multiplicative noise and periodic force to weaken the stability of unstable state;2.the additive noise induced transitions,the additive noise in the periodic force on the half cycle value would weaken the stability of unstable state,but in the period under the half cycle when the additive value the noise will enhance the stability of unstable state;correlation 3.multiplicative noise and additive noise induced transitions,multiplicative noise and additive noise are interrelated and periodic force will weaken the stability of metastable state.The effect of the periodic force parameters of the associated noise on the NES effect in the periodic force modulation(Logistic)system is studied.The results show that:1.The periodic force has the effect on stochastic systems similar to that of noise.That means the lifetime of metastable state also can be controlled by taking the value of periodic force.2.The stability of the metastable state is weakened by multiplicative noise and periodic force when the periodic force and multiplicative noise cooperate.The correlation between multiplicative and additive noise add periodic force also weaken the stability of metastable state,and the stability of metastable state can be enhanced by additive noise only when the second halfperiod value of the periodic force is taken. |
