Self-sustained activity in a small-world network of excitable neurons.

We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities p of directed random connections, a localized transient stimulus results either in self-sustained persistent activity or in a brief transient followed by failure. Averages over the quenched ensemble reveal that the probability of failure changes from 0 to 1 over a narrow range in p; this failure transition can be described analytically through an extension of an existing mean-field result. Exceedingly long transients emerge at higher densities p; their activity patterns are disordered, in contrast to the mostly periodic persistent patterns observed at low p. The times at which such patterns die out follow a stretched-exponential distribution, which depends sensitively on the propagation velocity of the excitation.

[1]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[2]  V. Mountcastle.  The columnar organization of the neocortex. , 1997, Brain : a journal of neurology.

[3]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[4]  Jian-Young Wu,et al.  Propagating Activation during Oscillations and Evoked Responses in Neocortical Slices , 1999, The Journal of Neuroscience.

[5]  L F Lago-Fernández,et al.  Fast response and temporal coherent oscillations in small-world networks. , 1999, Physical review letters.

[6]  M. Newman,et al.  Mean-field solution of the small-world network model. , 1999, Physical review letters.

[7]  P. Goldman-Rakic,et al.  Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. , 2000, Cerebral cortex.

[8]  D. Lewis,et al.  Horizontal synaptic connections in monkey prefrontal cortex: an in vitro electrophysiological study. , 2000, Cerebral cortex.

[9]  M B Jackson,et al.  Epileptiform discharges with in-vivo-like features in slices of rat piriform cortex with longitudinal association fibers. , 2001, Journal of neurophysiology.

[10]  Fernando J. Corbacho,et al.  Connection topology dependence of synchronization of neural assemblies on class 1 and 2 excitability , 2001, Neural Networks.

[11]  G B Ermentrout,et al.  Bistability in pulse propagation in networks of excitatory and inhibitory populations. , 2001, Physical review letters.

[12]  German Barrionuevo,et al.  Synaptic targets of the intrinsic axon collaterals of supragranular pyramidal neurons in monkey prefrontal cortex , 2001, The Journal of comparative neurology.

[13]  D. McCormick,et al.  On the cellular and network bases of epileptic seizures. , 2001, Annual review of physiology.

[14]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[15]  A. Pekalski,et al.  Ising model on a small world network. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[17]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[18]  Alejandro D Sánchez,et al.  Nonequilibrium phase transitions in directed small-world networks. , 2002, Physical review letters.

[19]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[20]  Resonance in periodically inhibited reaction-diffusion systems , 2002 .