Investigation of emergence of target wave and spiral wave in neuronal network induced by gradient coupling

Abstract

Distinct rhythm and self-organization in collective electric activities of neurons could be observed in a neuronal system composed of a large number of neurons. It is found that target wave can be induced in the network by imposing continuous local periodical force or introducing local heterogeneity in the network; and these target waves can regulate the wave propagation and development as pacemaker' in the network or media. A regular neuronal network is constructed in two-dimensional space, in which the local kinetics can be described by Hindmarsh-Rose neuron model, the emergence and development of ordered waves are investigated by introducing gradient coupling between neurons. For simplicity, the center area is selected by the largest coupling intensity, which is gradually decreased at certain step with increasing distance from the center area. It is found that the spiral wave and/or the target wave can be induced by appropriate selection of gradient coupling, and both waves can occupy the network, and then the collective behaviors of the network can be regulated to show ordered states. Particularly, the ordered wave can be effective to dominate the collective behavior of neuronal networks, even as the stochastic values are used for initial states. These results associated with the gradient coupling on the regulating collective behaviors could be useful to understand the self-organization behaviors in neuronal networks.