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Entrainment and chaos in the pulse-driven Hodgkin-Huxley oscillator | | Kevin K. Lin
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10 May 2005 | | Subject: | Dynamical Systems; Neurons and Cognition; Chaotic Dynamics MSC-class: 37N25 | math.DS nlin.CD q-bio.NC | | Abstract: | The original Hodgkin-Huxley model describes action potential generation in the squid giant axon and is a paradigm for conductance-based, excitable biological systems. Motivated by the recent theoretical work of Qiudong Wang and Lai-Sang Young, this paper examines the response of the Hodgkin-Huxley equations to low-frequency periodic pulsatile forcing. It is shown that 1. The pulse-driven Hodgkin-Huxley system exhibits a surprisingly wide range of qualitatively distinct behaviors, including stable entrainment (phase locking) to the input pulse train, transient chaos followed by entrainment, and fully chaotic behavior. 2. The pulse-driven Hodgkin-Huxley system prefers entrainment over chaos: most combinations of drive frequency and amplitude lead to entrainment instead of chaos. 3. These phenomena can be understood in terms of a general theory of kicked oscillators developed by Wang and Young, together with specific geometric structures in the Hodgkin-Huxley phase space. The concept of phase resetting curves, first introduced by Winfree, plays an important role in this context. This paper discusses a simplified version of the Ermentrout-Kopell adjoint method for computing phase resetting curves; it may be easier to implement in higher-dimensional settings. | | Source: | arXiv, math.DS/0505161 | | Services: | Forum | Review | PDF | Favorites | |
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