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Vol. 1, No. 1, pp. 105–114 c ○ 2002 Society for Industrial and Applied Mathematics Chaos in the Hodgkin–Huxley Model ∗

By John Guckenheimer and Ricardo A. Oliva

Abstract

Abstract. The Hodgkin–Huxley model was developed to characterize the action potential of a squid axon. It has served as an archetype for compartmental models of the electrophysiology of biological membranes. Thus the dynamics of the Hodgkin–Huxley model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods that can be applied to more complex models. This note demonstrates previously unobserved dynamics in the Hodgkin–Huxley model, namely, the existence of chaotic solutions in the model with its original parameters. The solutions are found by displaying rectangles in a cross-section whose images under the return map produce a Smale horseshoe. The chaotic solutions are highly unstable, but they are significant as they lie in the basin boundary that establishes the threshold of the system. Key words. Hodgkin–Huxley, chaos, action potential, horseshoe AMS subject classifications. 92C20, 37G35 PII. S1111111101394040 1. Introduction. The Hodgkin–Huxley model [15] for the action potential of a spaceclamped squid axon is defined by the four dimensional vector fiel

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.172.924
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