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Synchrony and Desynchrony in Integrate-and-Fire Oscillators

Department of Physics, The Ohio State University, Columbus, Ohio 43210, U.S.A.

DeLiang L. Wang

Department of Computer and Information Science and Center for Cognitive Science, The Ohio State University, Columbus, Ohio 43210, U.S.A.

Ciriyam Jayaprakash

Department of Physics, The Ohio State University, Columbus, Ohio 43210, U.S.A.

Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrate-and-fire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrate-and-fire oscillators. We illustrate that a LEGION architecture with integrate-and-fire oscillators can be similarly used to address image analysis.

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