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Chaotic burst synchronization in heterogeneous small-world neuronal network with noise. (English) Zbl 1203.05142

Summary: Chaotic bursting is a fundamental behavior of neurons. In this paper, global and local burst synchronization is studied in a heterogeneous small-world neuronal network of non-identical Hindmarsh-Rose (HR) neurons with noise. It is found that the network can achieve global burst synchronization much more easily than phase synchronization and nearly complete synchronization. Moreover, local burst synchronized clusters have already formed before global burst synchronization happens. We study the effect of the shortcut-adding probability and the heterogeneity coefficient on local and global burst synchronization of the network and find that the introduction of shortcuts facilitates burst synchronization while the heterogeneity has little effect. Moreover, we study the spatiotemporal pattern of the network and find that there is an optimal coupling strength range in which the periodicity of the network is very apparent.

MSC:

05C82 Small world graphs, complex networks (graph-theoretic aspects)
92B20 Neural networks for/in biological studies, artificial life and related topics
37N35 Dynamical systems in control
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