Observation of crises and bifurcations in the Hodgkin-Huxley neuron model

Abstract

With the changing of the stimulus frequency, there are a lot of firing dynamics behaviors of interspike intervals (ISIs), such as quasi-periodic, bursting, period-chaotic, chaotic, periodic and the bifurcations of the chaotic attractor appear alternatively in Hodgkin-Huxley (H-H) neuron model. The chaotic behavior is realized over a wide range of frequency and is visualized by using ISIs, and many kinds of abrupt undergoing changes of the ISIs are observed in deferent frequency regions, such as boundary crisis, interior crisis and merging crisis displaying alternately along with the changes changes of external signal frequency, too. And there are many periodic windows and fractal structures in ISIs dynamics behaviors. The saddle node bifurcation resulted collapses of chaos to period-12 orbit in dynamics of ISIs is identified. © Springer-Verlag Berlin Heidelberg 2005.