The Best Coupled Matrix Of The Stochastic Resonance Of System

The concept of Stochastic resonance was first put forward during the process of revealing the changing regulations of climates in ancient times. In certain nonlinear systems, the phenomenon that appropriate disturbance of noises can strengthen the system signal outputs was defined as Stochastic Resonance(SR). In modern SR theory, coupled system, one of the most popular subjects, has found its applications in many fields such as Physics, Chemistry, Biology, and etc. Some primitive theories were obtained by Benzi and his cooperators. Then, SR was studied in two dimensional, or more in general, N dimensional cases by Linder et al. It was discovered that the occurring of SR was the result of the interactions of periodic force, white noise and coupled system. It was stated in the literature [25] that SR in coupled system would be stronger than that in single system and some interesting phenomena could also occur in coupled system.Based upon the above studies, this paper aims to investigate orbit traits and SR of the Langevin equation with noise disturbances, without noise disturbances, and in coupled system. It is discovered that SR can be strengthened by the appropriate disturbance of stochastic force, especially in coupled systems.The emphasis of this paper was on the effects on SR caused by different coupled matrices .It turns out that the differences of coupling matrix have great influence on system energy. However, stochastic force can't take effect if the matrix elements are too big. SR will be much significant if matrix elements are differ from each other. By using the genetic algorithm, the optimal couphng matrix (3 times 3 and 5 times 5) was found in this paper. It is shown that the peak of the power spectrums of the system with the optimal coupling matrix is much bigger than the system with some random interactions.