Transient termination of spiking by noise in coupled neuronsB. S. Gutkin1, J. Jost2 and H. C. Tuckwell2
1 Group for Neural Theory, Départment des Etudes Cognitives, Ecole Normale Supérieure, Collège de France 5, rue d'Ulm, 75005 Paris, France
2 Max Planck Institute for Mathematics in the Sciences - Inselstr. 22, 04103 Leipzig, Germany
received 11 September 2007; accepted in final form 16 November 2007; published January 2008
published online 14 December 2007
We examine the effects of stochastic input currents on the firing behavior of two excitable neurons, coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling can cause sustained firing or oscillatory behavior which is necessarily antiphase. Additive Gaussian white noise can transiently terminate the oscillations by moving the dynamics away from the stable limit cycle. Further application of the noise may return the system to spiking activity. When the noise is sufficiently weak, the durations of the times spent in the oscillating and the resting states are strongly asymmetric. Hence weak noise tends to stop the spiking activity. When the noise is stronger, the periods of cessation of activity tend to be smaller. We numerically investigate an approximate basin of attraction, , of the periodic orbit and use Markov process theory to explain the firing behavior in terms of the probability of escape of trajectories from .
05.40.Ca - Noise.
84.35.+i - Neural networks.
87.16.Ac - Theory and modeling; computer simulation.
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