Research On Cluster Synchronization Of The Networked Coupled Oscillators

Synchronization is a widely observed in nonlinear science. There are all kinds of synchronous phenomenon whether in nature and artificial theory or environment. Synchronization means that two or more than two variables maintain definite relative relationship in the process of transformation over time. People made a lot of achievements, which had played a positive guiding role on real life. Along with that the research of the low dimensional coupling nonlinear system is more systematic and mature gradually, people found that the coupling system with a large number of nonlinear oscillators can exhibit more complex behavior, which also have certain rules to follow. In recent study, there is more and more interest in cluster synchronization, and more application to brain science, ecological science and engineering, communication engineering etc.Based on this consideration, this paper considers the research on cluster synchronization of coupled oscillators network, analyses different types of the network to achieve the cluster synchronization state and the special cluster synchronization of the neural networks with proportional delay. There are the corresponding theoretical results and the results from the simulation in this paper.This paper mainly has two results:first of all we mainly analyze the dynamic process of different coupling oscillator system to reach cluster synchronization. Then we raise network analysis of different dynamics coupled harmonic oscillators to reach cluster synchronization, which are the undirected coupled harmonic oscillator system, the directed coupled harmonic oscillator system and the coupled harmonic oscillator with time delay. Through the simulation of three kinds of system simulation, we obtain the influence factors of cluster synchronization rate, and have a deeper understanding of time delay. Then we mainly analyze the cluster synchronization problem of neural network with proportional delay. We propose the model of the neural networks with proportional delay to achieve cluster synchronization, and further get the sufficient conditions of cluster synchronization, which provides theoretical supports for the control of cluster synchronization.