Random System Of Non-equilibrium Phase Transitions, Particle Transport And Stochastic Resonance Study

The word 'noise' in our daily consciousness is associated with the term 'hindrance'. It was traditionally considered that the presence of the noise usually destory the order of the system. However, The phenomena of the fluctuation are typical for all real systems because of the internal perturbation of the system and the perturbation of environment. This phenomena can not be eliminated in principal. Recently, the development of the nonlinear science and statistical physics tell us that the presence of noise sources in nonlinear dynamical systems not only can give rise to the tiny change for the results of the original deterministic equation, but also can, unexpectedly, induce some new, complex phenomena that can not be exhibited at the absence of noise. At the same time, the disturbance of the irregular noise does not always destroy the order of the system. Contrary, it can play a constructive role, producing the coherent motion, and enhancing the degree of order in a nonlinear system under the proper condition. So, revealing the important effeces induced by noise in nonlinear system, studying conditions, machanism and application have been the important task for the development of the nonlinear science.In this thesis, the center problem that we will study are some physical phenomena that are induced by the presence of the noise, including transport of particles, the non-equalibrium transition(or phase transition), and stochastic resonance. The thesis consists of five chapters. In chapter one, firstly, we summarize the work that have been done by researchs at hame and abroad about some nonlinear system induced by noise, subsequently, we describe work that we will do. In chapter two, we mainly study the system drived by the temporal-spatial noise. The chapter is divided into two parts: in the first part, we study the system when the coupling among particles is zero. Here, even the potential is symmetry, the system can also exhibit the phenomenon of transport of particles. This is because of the correlation between noise and the space; in the second part, we study the system when the coupling among particles exist. Here, the system driven by the temporal-spatial noise and the force exhibit transport of particles, the anomalous hystereses, and non-equalibrium transition (or phase transition). The part is divided into two small parts: in the first small part, we maily study the transport of particles of the system driven by temporal-spatial noise. We have found that the coupling among different particles, temporal-spatial noise, the external force and the asymmetric potential are important gredients caused the transport of particles;in the second small part, we take example for the special system, then study transport of particles^ the anomalous hystereses, and non-equalibrium transition(or phase transition) of the system. In the chapter three, we study the transport of particles of the system subject to three-value poissonian noise, and analyze the mechanism caused transport. In the chapter four, we study the phenomena of stochastic resonance of the system driven by noise. The chapter is divided into two parts: in the first part, we study the phenomenon of stochastic resonance of the non-linear system driven by the O-U noise; in the second part, we study the phenomenon of stochastic resonance of the linear system driven by multiplicative asymmetric dichotomous noise, from the general definition and the extensive definition, respectively. In the chapter five, we, respectively, study three different temporal-spatial dichotomous noise, and drive out the master equations of the noise and the system driven by them.