Synchronization Of Multi-layer Chaotic System Network

The chaotic system network is a network which takes the dynamic system in chaotic state as a node and takes some interaction relationship between the systems as the connecting edge.The nodes in this network not only have their own dynamic behavior,but also are affected by other nodes in the network,so the whole network can show more complex characteristics,and then complete the modeling of complex system.Compared with single-layer networks,multi-layer networks are more widespread in reality.Therefore,multi-layer networks have great research significance.Synchronization phenomenon exists widely in various fields of nature and has a profound impact on people’s lives.Therefore,this paper focuses on the synchronization of multi-layer networks composed of chaotic systems.The nodes of the network are constructed at first.The items reflecting the properties of memristor and other non-linear items are introduced to Yang system,and a chaotic system which can change the number of the attractor scrolls by adjusting the parameters and the initial value of the state variables is presented.The chaotic attractor with single scroll,double scrolls and triple scrolls is obtained.Then the power spectrum,Poincaré cross section,Lyapunov exponent spectrum,bifurcation diagram and other methods were used to verify the chaotic characteristics of the system.After that,by employing the method of complex polynomial transformation to expand the scroll number of the system,a multi-scroll chaotic system capable of generating ring-shaped attractors is acquired.The number of scrolls of the attractor can be changed by adjusting the power of the complex polynomial.Then the synchronization of two nodes with different dynamic behaviors is realized.The chaotic system that can generate the ring-shaped multi-scroll attractor is used as the driving system to synchronize another chaotic system with a grid-shaped multi-scroll attractor.In this part,a method to realize the synchronization of multi-scroll chaotic system is proposed.As long as the multi-scroll system satisfies the specific construction conditions,the synchronization can be realized after the appropriate parameters are selected.Then the proposed method is applied to the synchronization of a six-scroll ring-shaped attractor system and a sixteen-scroll grid-shaped attractor system with external interference signals.After that,the chain synchronization of the ring-shaped multi-scroll system is observed by numerical simulation.After realizing the synchronization of the two chaotic systems,the synchronization of the multi-layer network composed of the nodes with the above two chaotic dynamic behaviors under different topological structures is studied.The network topology is divided into a planar network and a three-dimensional network.In the planar network,the synchronization of a four-layer network with the tree structure is realized.The synchronization problems when the nodes with the same dynamic behavior and different dynamic behaviors are studied.In the three-dimensional network topology,three-layer star-shaped networks are synchronized.Starting from the same and different conditions of the central node and the leaf node of each layer network,the chain synchronization phenomenon and the method of adding controller are applied to realize the synchronization of the network.