Coherence resonance in an autapse neuron model with time delay

We study the noise activated dynamics of a model autapse neuron system that consists of a subcritical Hopf oscillator with a time delayed nonlinear feedback. The coherence of the noise driven pulses of the neuron exhibits a novel double peaked structure as a function of the noise amplitude. The two peaks correspond to separate optimal noise levels for excitation of single spikes and multiple spikes (bursts) respectively. The relative magnitudes of these peaks are found to be a sensitive function of time delay. The physical significance of our results and its practical implications in various real life systems are discussed. All the numerical simulations in the present paper have been carried out with the help of the software packages XPPAUT 28 and DDE-BIFTOOL.29 XPPAUT also provides an interface to the continuation software package AUTO. 30 The authors thank C.S. Zhou for valuable discussions. JK acknowledges the support via his Humboldt-CSIR research award and the Network of Excellence BIOSIM of the European Union Contract LSHB-CT-2004-005137.