Homoclinic bifurcation in a Hodgkin–Huxley model of thermally sensitive neurons

TLDR

The control parameter for this model is the temperature. We study global bifurcations of the chaotic attractor in a modified Hodgkin–Huxley model of thermally sensitive neurons. The chaotic behavior occurs over a wide temperature range and is visualized via interspike intervals, revealing a homoclinic bifurcation of a saddle‑focus fixed point embedded in the chaotic attractors. We observe an abrupt increase in interspike intervals at a specific temperature, accompanied by intermittency that follows a universal scaling law for short‑interval trajectory segments, and experimental data from crayfish photoreceptors qualitatively confirm this bifurcation structure. © 2000 American Institute of Physics.

Abstract

We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics.