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Nonlinear dynamical mechanism underlying neuronal adaptation

Recent neurophysiological evidence suggests that the input-output relations of visual and auditory neurons are not static, but adaptive to the statistics of the stimuli. We investigate in this paper the possibility that the nonlinear dynamics of the neuron itself can explain a variety of adaptation phenomena. System identi ̄cation technique is applied to study the transfer function of Huxley-Hodgkin model in response to white noise stimuli and to explore whether the basic neuronal model exhibits the same adaptation phenomena as observed experimentally. We found that the transfer function of the HH model does adapt to the noise statistics of the stimuli, and concluded many observed adaptation phenomena in neural systems can be attributed to the bifurcation nonlinear dynamics of the spiking neurons. Our result demonstrates that adaptation is a consequence of the cooperative interaction between noises and the nonlinear dynamics of the neuron, and can be understood in terms of a class of physical phenomena called coherent resonance. Coherence resonance is directly responsible for shaping neuronal transfer or tuning functions dynamically in response to the stimulus statistics of the environment. Analysis of the Leaky Integrate-and̄re model traces the CR phenomena to adaptation of threshold in bifurcation dynamics as a function of noise, suggesting coherence resonance and hence adaptive phenomena exists in neurons individually and collectively.