Quantification of similarity using amplitudes and firing times of a hodgkin-huxley neural response

Abstract

Periodic stimuli are known to induce chaotic oscillations in the squid giant axon for a certain range of frequencies. This behaviour is modelled by the Hodgkin-Huxley equations when a periodic stimulus is applied. The responses resulting from chaotic neural dynamics have irregular inter-spike intervals and fluctuating amplitudes. These characteristics are absent in steady state responses of the Hodgkin-Huxley neuron which are generated using a constant current stimulus. It is known that firing time information is adequate to estimate similarity of steady state responses; however, in the presence of chaotic oscillations, similarity between neural responses cannot be estimated using firing time alone. The results discussed in this paper present a quantification of the similarity of neural responses exhibiting chaotic oscillations by using both amplitude fluctuations and firing times. We relate the similarity thus obtained between two neural responses to their respective stimuli. Identical stimuli have very similar effect on the neural dynamics and therefore, as the temporal inputs to the neuron are the same, the occurrence of identical chaotic patterns result in a high estimate of similarity for the neural responses. Estimates of similarity are compared for periodic stimuli with a range of inter-spike intervals. © 2011 Springer Science+Business Media B.V.