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Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons. (English) Zbl 0990.92003

Summary: 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.

MSC:

92C20 Neural biology
37N25 Dynamical systems in biology
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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