Synchronizations of chaotic neuronal networks under different couplings

Abstract

The synchronization of a two-dimensional (2D) neuronal network is investigated, based on the dynamical model of Hindmarsh-Rose neuron. In order to know the effects of different types of coupling on the synchronization of a network, we propose three coupling schemes. They are the general feedback coupling, the hierarchical feedback couplings with and without local mean field. The numerical results show that when the neighbor coupling strength is small, the hierarchical feedback couplings with and without local mean field can achieve local and global synchronizations of the network, whereas the general feedback coupling cannot achieve global synchronization. Different couplings generate different patterns in the corresponding network, so that the processes of the transition from asynchronization to synchronization in the networks are different. With the increase of coupling strength, the synchronization in the network with the general feedback or hierarchical feedback couplings is suddenly established, and the networks exhibit different coherent patterns that are aperiodic before the global synchronization occurs. However, the network with hierarchical feedback couplings and local mean field exhibits the different synchronous processes. The neurons in the same layer first achieve the transition from bursting synchronization to global synchronization, leading to the formation of target wave. Then, the synchronization region gradually expands from the center of the network. Finally, the whole networks can achieve synchronization. These results show that the lossless signal transmission can be achieved only if the appropriate coupling is applied. In addition, we find that the hierarchical feedback coupling with local mean field can facilitate synchronization.