Study On Hyperchaos And Hyperchaos Synchronization Mathod For Cellular Neural Networks

Cellular neural networks(CNN) are large-scale non-linear dynamical systems.They can process signal parallelly in real time with high speed, and are easy to realizewith very large scale integration. Excellent signal processing performance of CNNmakes CNN a hot research area in recent years. At the same time, the CNN arenon-linear dynamic systems, one can expect interesting phenomena (“bifurcations”)and complex (“chaotic”) dynamics to occur in such networks.In this thesis, we study the generation and synchronization of chaotic behavior inCNN. Then, we analyze the character of sensitive to initial inputs of chaos in CNNwith numerous analysis. The results show that there are significant clustering in thecharacter of sensitive to initial inputs. Concrete work is summarized as follows：Firstly, we establish4-order,5-order and6-order chaotic cellular neural networksand hyperchaotic cellular neural networks, and analyse the chaos and hyperchaos withphase space and lyapunov exponents.Then, we analyse the character of initial inputs sensitivity of chaos in cellularneural networks with proper experiment. The inputs of the chaostic CNN are twoinitial values with tiny differences. The outputs are two distinct signals. We get a newsignal after subtracting one signal from the other.Calculate the energy of the new signal.We found clustering performance in the energy of the new signal.Moreover, based on the clustering performance, a new algorithm for determiningchaos is proposed, named SLE. In the new algorithm, we can eliminate a majority ofcellular neural networks with no chaos according to the clustering performance, onlywhen the cellular neural networks have the performance of clustering, we need tocalculate lyapunov exponents, and determine whether chaos phenomena turned up inthe system by lyapunov exponents.Finally, verify the feasibility of chaotic synchronization of cellular neuralnetworks by traditional synchronization methods, such as chaotic synchronization ofdriving-response, active and passive decomposition approach, mutual couplingsynchronization method, feedback control method and state observer method. According to the simulation results, we know that all of the above five synchronizationmethods can be used in the CNN chaos system.