Reconsruction Of Hodgkin-huxley Neuronal System From Interspike Intervalts

The interspike interval (ISI) data based on the spike train manifeststhe external characteristic of Hodgkin-Huxley neuronal system well. Inrough analogy with Takens’ theorem for attractor reconstruction from timeseries，we carry out reconstruction of Hodgkin-Huxley neuronal systemfrom interspike intervals. With reference to the delay-coordinate method,we adopt interspike interval vectors to reconstruct the space phase.In this process， corresponding theory analysis and numericalsimulation are made which can choose the two key-parameters: embeddingdimension and time-delay. In addition, we apply a simple version of anearest-neighbor prediction algorithm to verify the assumption that thenonlinear deterministic structure of the dynamics is preserved in the ISI’s.On the basis of the theory that interspike intervals can be forecast frompast history, we show that deterministically driven ISI series can bedistinguished from stochastically driven ISI series on the basis ofprediction error.