Study On A Two-dimensional Small-world Chaotic Neural Network

Artificial neural network has so many excellent features in the simulation of the real neural network, that it has always been a hot research area. Because of the rich dynamics and potential application value, the chaotic neural network has become an important research field in artificial neural network.Nowadays, there are mainly two directions in the research of neural network:the one is the topology of neural network, to seek for the most likely connection methods on the connection diagram. However, the studies recently take most attention on the chain or cyclic structure in small scale, but less on the large scale two-dimensional small world network; the other one is the neuron dynamics models. The past researches mainly focused on the Hodgkin-Huxley model and Nagamu-Sato model, however, there were relatively fewer study on the Aihara neuron model which is based on bio-electricity experiment.In this paper, we firstly construct a two-dimensional closed boundary small-world network, and apply Aihara chaotic neuron model and Hebb learning rules to study its dynamics. Then, we add some isolated nodes into the topology, and studied the influence on global synchronization of the network. The result shows that if the isolated nodes accounted for about1.5%of the total nodes, the network synchronizability will be markedly damaged. Finally, we study the effect of network connectivity probability, coupling strength and node average connection strength on its synchronization. The study found that it is not conducive to the synchronization if the parameters above are too large or too small, but has appropriate values.The results of this study can help to understand the neural information transmission mechanism, and provide some new ideas for the further revealing the mystery of the brain.