The Study Of Signal Power Amplification Process In The Time-delayed Bistable Systems And Anomalous Transport Behaviors Of The Inertial Motors

In this thesis, stochastic resonance (SR) phenomenon and anomalous trans-port behaviors in periodically driven nonlinear systems were investigated. First, the background, actuality and related theory of the stochastic resonance and anomalous transport were comprehensively reviewed. Then, the SR in time-delayed bistable systems and the anomalous transport behaviors in Brownian motor and vibrational motor were systematically and deeply investigated. The signal power amplification was employed to characterize SR phenomenon, while the current-characteristic was used to describe the anomalous transport behavior. Detailed research results are summarized as follows:The effects of time delay on the non-adiabatic regime of SR in a bistable system was investigated. Two forms of time delay were discussed respectively. Simulation results indicated that:(1) For intermediate level of frequency Ω of the periodic signal, the typical behavior of SR is lowered monotonically by increasing the delay time τ; for large Ω, τ weakens the SR behavior and then enhances it, with a non-monotonic behavior as a function of time delay.(2) Time delay induces SR for the above-threshold driving amplitude, where no such resonance exists in the absence of time delay.(3) Time delay induces a transition from bimodal to unimodal configuration of signal power amplification.(4) Varying the particular form of time delay results in different phenomena.The stochastic resonance in an under-damped bistable system with time delay was studied. Numerical simulation results are as follows:(1) For moderate fre-quency of the periodic driving, the stochastic resonance is decreased monotonically by increasing the delay time, but at high frequency, the reverse-resonance trans-forms into the stochastic resonance induced by time delay.(2) Damping coefficient has a critical value for which the stochastic resonance is optimum.(3) Stochastic multi-resonance emerges when the signal power amplification as a function of the driving frequency.The stochastic resonance in a bistable system with global time delay was studied. Main results read:(1) For a periodic signal with low driving frequency, the typical behaviour of the SR is lowered monotonically by increasing the delay time; for moderate driving frequency, delay time enhances the SR behaviour and then weakens it, with a critical value at which the SR is optimum.(2) Multiplicative noise intensity D and additive noise intensity a have different influences on the SR performance, viz D enhances the SR monotonically while a enforces the SR initially and then restrains it.(3) Correlation intensity λ between the two noises always weakens the SR behaviour of the system.Control of negative mobility phenomenon in the Brownian motor via time delay and biharmonic mixing was explored. Within tailored parameter regimes, the increasing delay time diminishes the noise-induced absolute negative mobility (ANM) and the deterministic ANM while it induces the ANM in a normal trans-port regime. When an asymmetric parameter is added in the periodic potential, the presence and absence of multiple current reversals are controlled by manipu-lating the delay time. By taking advantage of the biharmonic mixing method, one can obtain the velocity opposite to the external force at a relative high tempera-ture. Meanwhile, the transport velocity can be revered to be opposite to the bias by increasing the random.The model of vibrational motor was first put forward and its anomalous trans-port behaviors were considered. An anomalous transport phenomenon termed ab-solute negative mobility was observed in a vibrational motor, where an additional time-periodic signal filling the role usually played by noise in a Brownian mo-tor. Within tailored parameter regime, the absolute negative mobility behavior is maximized at two regimes upon variation of the bias. The observed absolute negative mobility still survives at a wide range of the driving strength and an-gular frequency of the additional signal. Three anomalous transport phenomena were theoretically predicted within the parameter regimes controlled by determin-istic attractors. By manipulating the amplitude of the additional periodic signal, absolute negative mobility, negative nonlinear mobility and differential negative mobility were observed. Coexisting attractors are responsible for these anomalous transport phenomena.