Synchronization Of Rossler Chaotic Dynimical System In Complex Network

The network is deemed to a kind of mathematical model, because it can reflect objective world really. Along with the science and technology development, people know complex network in really world gradually, and find it isn't completely regular or completely random. The complex network has become a bit hot in many research fields. The synchronization of complex network is an advancing topic in physical realm. The research of this field can explain many realistic network mechanisms accurately, there is a huge applied potential.In this paper, we first make the smallest world network model and NW small world network model as research target; pass the numerical simulation to study the synchronization problem of complex dynamical system in complex network model. Then, we confirm the result of numerical experiment by the theoretic analysis. The fundamental works are summarized as follows:In the first part, we introduce a new network model—the smallest world network model. We carry out the synchronization of the Rossler dynamical system in isomorphic model of the smallest world network by numerical experiment, then, passing the theories analysis, we can verify the synchronous stability and the robustness. Draw the condition which the network can arrive synchronization.In the second part, we make isomorphic model of the smallest world network as foundation, construct isomerous model of the smallest world network: we replace the central node with Lorenz oscillator. We research the synchronization of isomerous dynamical system by numerical simulation, and prove the result of numerical experiment by theoretical method. The third part is mainly connected with NW small world network. We construct a NW small world by special method. Let nodes of nearest neighbor couple by both-way intercoupling, but make long-range connection couple by one-way coupling. We can find the dynamical system can carry out synchronization in some condition. Then, passing the theory proving, make out this model differs from the nearest neighbor network. And we verified the Rossler dynamical system of this model having synchronization stability.