Stochastic Resonance In Bistable Systems, Monostable Systems, Coupled Systems And Chaotic Systems.

In this thesis, we investigate the phenomenon of stochastic resonance (SR) in different systems, such as bistable systems, monostable systems, coupled systems with and without periodic driving as well as chaotic systems. In order to distinguish physical reasoning from rigorous mathematical proof, as well as unpublished results from the published ones, we divide our statements into three parts:I. physical describing of SR;II. Mathematic proof of some theorem found first in the simulation of SR;III. Our published paper about SR without periodic driving in several situations.In part I, we concentrate our attention only to SR with periodic force, referring SR without periodic driving to Part III.Chapter 1 is the discussion for bistable systems driven by a periodic signal and white noise, we first give a qualitative analysis of the existence and the number of limit cycles by considering its equivalent system in the deterministic case on a cylinder. Then we numerically manifest that the number of the limit cycles and their relative position are crucial for the happening of SR. Subthreshold as well as suprathreshold driving signals are both taken into account.Chapter 2 is the investigation of SR for monostable systems without periodic driving. The cases for a single oscillator system and for a coupled system are both taken into account. For the former case, we clarify the mechanism of SR-like phenomenon on a unit circle. As for the coupled system without periodic driving, besides numerically showing the array enhanced SR, we pointed...