Cluster Synchronization And Cluster Synchronization Transition Of Module Neuron Network System

A large number of neurons in the cerebral cortex through complex connection constitute neural networks. The brain functions are closely related to dynamical behavior of neuronal networks. Researches have indicated that neural information processing in the brain is based on the coordinated interactions of large numbers of neurons within different brain areas. Synchronization behavior of coupling neurons plays a key role in brain information processing. Due to the existence of the synaptic cleft and the finiteness of neural information propagation speed, time delay in the neural network is also a factor that cannot be ignored. In recent years, physiological studies have showed that brain neuronal network in structure with modularization properties. Therefore, under the influence of factors such as delay, investigating burst synchronization of modular neuronal network and the related dynamic problems have important theoretical significance. By constructing modular neuronal network system, using the theory and methods of nonlinear dynamics and numerical simulation, this paper is devoted to investigating the properties of burst synchronization and burst synchronization transitions in modular neuronal network. The main contents and conclusions are as follows:1. By constructing a model of modular neuronal network whose individual elements are Courbage-Nekorkin-Vdovin neurons, the subnetworks are BA scale-free or NW small-world networks. The global burst synchronization and its evolution process are explored in modular neuronal network. Numerical results have demonstrated that, upon increasing intra-coupling strength, the global synchronization processes of modular neuronal network have been presented, all neurons in the modular network firstly burst in a desynchronous pattern, then burst synchronization within each subnetwork is followed, finally global burst synchronization is formed by the bursting activities on each subnetwork moving forward in harmony. At the same time, the results suggested that inter-connection probability has significant influence on burst synchronization in modular neuronal network. It is found that global burst synchronization can be promoted by large inter-connection probability and hindered by small inter-connection probability. Moreover, it is also found that above results has nothing to do with the number of neurons in subnetworks when the network size is not changed. In addition, it is also revealed that, the more the number of subnetworks, the more easily to achieve global burst synchronization for modular neuronal network.2. By constructing a model of modular neuronal network is composed of NW small-world networks. The effects of coupling strength and coupling delays on the burst synchronization dynamics are investigated. The numerical result has shown that appropriate intra-coupling strength can induce burst synchronization in modular neuronal network when the coupling term without delay. When time delay is introduced to the coupling term, it is found that delay can induce the transitions of burst synchronization emerging in the modular neuronal network. Moreover, all these transitions to burst synchronization occur approximately at integer multiples of average oscillation periods of all the neurons contained in the modular neuronal network. Additionally, delay-induced burst synchronization transitions are confirmed to be robust to the interconnection probability, the intra-coupling strength, the number of neurons in each subnetwork and the network size.