Synchronization Analysis And Simulation On Regular Coupled Neural Networks

As the basic structure and functional unit of the nervous system,neuron has Complex nonlinear properties,such as bifurcation,chaos and periodicity.However,a single neuron generally cannot complete the processing of information,and must to be coupled with other neurons to form a cluster of neurons to carry out.Synchronization,as a typical manifestation of neuron cluster discharge,is important for neural information processing Mechanism.Therefore,the study of neuron synchronization phenomenon is particularly important.In this paper,we mainly studies firing patterns and the phase synchronization and complete synchronization characteristics of the electrically coupled Hindmarsh-Rose model,the main results obtained as follows.Chapter 3 studies firing patterns and dynamics behavior and the phase synchronization of two coupled Hindmarsh-Rose models with time delay.Firstly,we regulated the value of DC strength,AC frequency and the parameter ,and then study the effects on neuronal firing activities by numerical simulation.In accordance with the ISIs bifurcation diagram,we can further study the transformation between different kinds of firing patterns which contains typical nonlinear dynamic phenomenon,such as periodic bifurcation,inverse cycle bifurcation,inverse period-doubling bifurcation,chaos phenomena.Secondly,by adjusting the coupling strength,we have found three special phase cases which are respectively out-of-phase synchronization,asynchronous state and in-phase synchronization in the electrically coupled Hindmarsh-Rose neuron models.Further,it is found that there is a complex synchronous transition behavior between the electrically coupled Hindmarsh-Rose neurons by continuously varying the coupling strength and the phase difference exhibit a period-doubling bifurcation phenomenon and under certain parameter values,though the coupling strength is very small,the coupled neurons also go into in-phase synchronization.Chapter 4 studies the complete synchronization characteristics of the neural network system composed of N electrically coupled Hindmarsh-Rose neurons.Firstly,the network model composed of N electrically coupled with symmetric connection is constructed.Secondly,through introducing appropriate error variable,we transform the stability of synchronization manifold into that of null solution of error equations.Through constructing a suitable Lyapunov function as well as applying matrix theory,the relative criterion is theoretically provided for global asymptotic synchronization and global exponential synchronization of Hindmarsh-Rose neural networks.Then,we consider the chain,ring,star and global connection system,and analyze their synchronization stability.Further,the theoretical result shows the influence of neuron numbers and connection types in neural network on synchronization.Numerical simulations test the reliability of the results in this paper.