Propagation of Bursting Oscillations in Coupled Non-homogeneous Hodgkin–Huxley Reaction–Diffusion Systems

  • B. AmbrosioEmail author
  • M. A. Aziz-Alaoui
  • A. Balti
Original Research


In this paper, we consider networks of reaction–diffusion systems of Hodgkin–Huxley type. We give a general mathematical framework, in which we prove existence and unicity of solutions as well as the existence of invariant regions and of the attractor. Then, we illustrate some relevant numerical examples and exhibit bifurcation phenomena and propagation of bursting oscillations through one and two coupled non-homogeneous systems.


Complex dynamical systems Hodgkin–Huxley equations Reaction–diffusion systems 



The authors would like to thank Région Normandie and FEDER XTERM for financial support.


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2017

Authors and Affiliations

  1. 1.Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCNLe HavreFrance

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