Stochastic oscillator death in globally coupled neural systems

초록

We consider an ensemble of globally coupled subthreshold Morris-Lecar neurons. As the coupling strength passes a lower threshold, the coupling stimulates coherence between noise-induced spikings. This coherent transition is well described in terms of an order parameter. However, for sufficiently large J, "stochastic oscillator death" (i.e., quenching of noise-induced spikings), leading to breakup of collective spiking coherence, is found to occur. Using the techniques of nonlinear dynamics, we investigate the dynamical origin of stochastic oscillator death. Thus, we show that stochastic oscillator death occurs because each local neuron is attracted to a noisy equilibrium state via an infinite-period bifurcation. Furthermore, we introduce a new "statistical-mechanical" parameter, called the average firing probability (P-f) over bar and quantitatively characterize a transition from firing to non-firing states which results from stochastic oscillator death. For a firing (non-firing) state, (P-f) over bar tends to be non-zero (zero) in the thermodynamic limit. We note that the role of (P-f) over bar for the firing-nonfiring transition is similar to that of the order parameter used for the coherence-incoherence transition.

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