The Study On The Inflence Of Parameter Noise On One-Dimensional Coupled Map Lattices

The complicated long-term state is very common in the nature systems of which chaos is very typical. Chaos initiates meticulous study of the complicated evolutive behavior and explodes the traditional concept of being forcasted to the determinate evolvement. As any system in the reality exists in the noise surroundings, we should take the affect of noise very seriously if the noise is inevitable and continual. Now it has been already realized that there is some similarity between noise and chaos . People has the great interest to the noise affect on the chaos systems, especially the noise affect on the Spatiotemporal chaos.Taken the one-dimensional coupled map lattices(CMLs) which is introduced as a simple model with the essential features of spatiotemporal systems as our study model, the affect of parameter noise on one-dimensional coupled map lattices and stochastic synchronization has been studied in this paper. The main results are listed as follows:1 In the first section we summarize the progress in the chaos study and point out that study of chaos deeply is promoting the formation of the complex science. The basic tools for the study of chaos and the importantfield of chaos application-chaos control and synchronization areintroduced compactly. At the same time , we emphases expatiating the application of the noise affect on chaos control and synchronization.2 The parameter noise existing in the one-dimensional coupled map lattices is considered and different kinds of noise are gived. The numerical computation of The Maximum Lyapunov Exponent (MLE) has been studied which decided whether the system exists in the chaos state. We analyze that if the MLE of random CMLs is negative, there exits the possibility of driving the two CMLs to synchronize.3 we take the CMLs of few-body and many-body as our study model. The change of state of CMLs under the noise affect by the MLE is studied and we found there exit systems parameter fields very sensitive to noise which show complicated behavior. Local noise is very difficult to change the state of whole system which has the ability of standing against the noise spontaneously.4 we study the synchronization of CMLs under the noise driving and support our forecast to some extent which also express the complicated behavior. The synchronization is not only decided by the MLE ,but also decided by the range of the random negative fluctuation . The possibility for synchronization of CMLs will increase with the enlarge the negative random fluctuation range. During this course, synchronization windage will show the structure along the time steps, it means systems tend to order little by little. We also find the little noise can induce the CMLs toperiodic state or chaos.5 we study the synchronization process and find the global synchronization is a gradual process that the local synchronization or cluster synchronization appear firstly. In the some limited precision, we can find the local synchronization in the loss of synchronization of whole CMLs systems. At the same time ,it exits a weaker local synchronization-local phase synchronization which means the phase of corresponding lattices is locked, but state variable is different. Further more ,the stability of the local lattice is probed into and the long-term evolutive behavior of the local lattice in the noise surroundings can be forecast effectively through the local characteristic exponent defined by this article.This article obtained some results of the CMLs how to response the parameter noise .At same time, the synchronization under the parameter noise driving can be obtained through this article study . The inherent mechanism about the synchronization under the parameter noise driving and local synchronization phase synchronization will need to farther study deeply.This Project is supported by the National Natural Science Foundation (Grant No.10147201)...