Forced Oscillations and Routes to Chaos in the Hodgkin-Huxley Axons and Squid Giant Axons

  • K. Aihara
  • G. Matsumoto
Part of the NATO ASI Series book series (NSSA, volume 138)


Nonlinear responses of a neural oscillator to sinusoidal force are analysed theoretically with the Hodgkin-Huxley equations and experimentally with squid giant axons.

First, the periodically forced oscillations in the nerve membranes are qualitatively classified into (1) synchronised oscillations, (2) quasi-periodic oscillations and (3) chaotic oscillations by examining the Poincaré sections and the return maps.

Second, it is confirmed that there exist the three types of routes to the chaos, namely, (1) the successive period-doubling bifurcations, (2) the intermittency and (3) the collapse of the quasi-periodicity. The global structure of the three routes and many Arnold’s tongues of the synchronised oscillations in the parameter space is also examined.

Last, simple mapping models of the neural responses are discussed.


Bifurcation Diagram Chaotic Oscillation Giant Axon Neural Oscillator Squid Giant Axon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • K. Aihara
    • 1
  • G. Matsumoto
    • 2
  1. 1.Department of Electronic Engineering Faculty of EngineeringTokyo Denki UniversityKanda Chiyoda-ku Tokyo 101Japan
  2. 2.Electrotechnical LaboratoryTsukuba Science CityNiihari-gun Ibaraki 305Japan

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