Synchrony and Desynchrony in Networks of Locally Coupled Wilson-cowan Oscillators

In this Chapter, we study networks of locally coupled Wilson-Cowan (W-C) oscilla-tors [Wilson and Cowan, 1972]. The W-C oscillator is a two variable system of ordinary differential equations and represents an interacting population of excitatory and inhibitory neurons. The amplitudes of the variables symbolize the proportion of each population of neurons that is active. We study these equations because they represent neuronal groups, which may be the basic processing units in the brain [Edelman, 1987]. The W-C equations have a large number of parameters, which allow for a wide range of dynamics. These equations have been used widely in modelling various brain processes [Feldman and Of particular relevance is a study by Cairns et al. [Cairns et al., 1993], which indicates that synchronization is possible with these equations. Despite extensive studies on W-C oscillators, it remains unclear to whether or not a locally coupled network can exhibit synchrony. It is also unknown how desynchronization can be achieved in such a network. We study locally coupled networks because globally coupled networks lack topologi-cal mappings [Sporns et al., 1989, Chawanya et al., 1993]. Specifically, in a two-dimensional network of oscillators, all-to-all couplings indiscriminately connects multiple objects. All pertinent geometrical information about each object, and about its relationships with other objects is lost. This information should be preserved if the network is to be used for segmentation and object recognition. Local couplings simply and efficiently preserve these spatial relationships.