Fast convergence of spike sequences to periodic patterns in recurrent networks.

The dynamical attractors are thought to underlie many biological functions of recurrent neural networks. Here we show that stable periodic spike sequences with precise timings are the attractors of the spiking dynamics of recurrent neural networks with global inhibition. Almost all spike sequences converge within a finite number of transient spikes to these attractors. The convergence is fast, especially when the global inhibition is strong. These results support the possibility that precise spatiotemporal sequences of spikes are useful for information encoding and processing in biological neural networks.

[1]  Vreeswijk,et al.  Partial synchronization in populations of pulse-coupled oscillators. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Dezhe Z Jin,et al.  Fast computation with spikes in a recurrent neural network. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  J J Hopfield,et al.  Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[4]  J. Hopfield,et al.  Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements. , 1995, Physical review letters.

[5]  Bottani.  Pulse-coupled relaxation oscillators: From biological synchronization to self-organized criticality. , 1995, Physical review letters.

[6]  Richard Hans Robert Hahnloser,et al.  An ultra-sparse code underliesthe generation of neural sequences in a songbird , 2002, Nature.

[7]  H S Seung,et al.  How the brain keeps the eyes still. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[8]  G B Ermentrout,et al.  Fine structure of neural spiking and synchronization in the presence of conduction delays. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Gerstner.  Rapid phase locking in systems of pulse-coupled oscillators with delays. , 1996, Physical review letters.

[10]  David Golomb,et al.  The Number of Synaptic Inputs and the Synchrony of Large, Sparse Neuronal Networks , 2000, Neural Computation.

[11]  G. Laurent.  A systems perspective on early olfactory coding. , 1999, Science.

[12]  Germán Mato,et al.  Synchrony in Excitatory Neural Networks , 1995, Neural Computation.

[13]  Stephen Coombes,et al.  Dynamics of Strongly Coupled Spiking Neurons , 2000, Neural Computation.

[14]  K. Zhang,et al.  Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[15]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[16]  Carson C. Chow.  Phase-locking in weakly heterogeneous neuronal networks , 1997, cond-mat/9709220.

[17]  Sompolinsky,et al.  Pattern of synchrony in inhomogeneous networks of oscillators with pulse interactions. , 1993, Physical review letters.

[18]  G. Laurent,et al.  Short-term memory in olfactory network dynamics , 1999, Nature.

[19]  B. M. Fulk.  MATH , 1992 .

[20]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[21]  W. Gerstner,et al.  Time structure of the activity in neural network models. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.