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We study the dynamical states that emerge in a small-world network ofrecurrently coupled excitable neurons through both numerical and analyticalmethods. These dynamics depend in large part on the fraction of long-rangeconnections or `short-cuts' and the delay in the neuronal interactions.Persistent activity arises for a small fraction of `short-cuts', while atransition to failure occurs at a critical value of the `short-cut' density.The persistent activity consists of multi-stable periodic attractors, thenumber of which is at least on the order of the number of neurons in thenetwork. For long enough delays, network activity at high `short-cut' densitiesis shown to exhibit exceedingly long chaotic transients whose failure-timesaveraged over many network configurations follow a stretched exponential. Weshow how this functional form arises in the ensemble-averaged activity if eachnetwork realization has a characteristic failure-time which is exponentiallydistributed.Comment: 14 pages 23 figure

Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons