title: Localized nonlinear excitations in diffusive Hindmarsh-Rose neural networks.
abstract: We study localized nonlinear excitations in diffusive Hindmarsh-Rose neural networks. We show that the Hindmarsh-Rose model can be reduced to a modified Complex Ginzburg-Landau equation through the application of a perturbation technique. We equally report on the presence of envelop solitons of the nerve impulse in this neural network. From the biological point of view, this result suggests that neurons can participate in a collective processing of information, a relevant part of which is shared over all neurons but not concentrated at the single neuron level. By employing the standard linear stability analysis, the growth rate of the modulational instability is derived as a function of the wave number and systems parameters.
authors.affiliation: Complex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea-Cameroon.
authors.forename: F M
authors.initials: FM
authors.lastname: Moukam Kakmeni
authors.affiliation: Complex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea-Cameroon.
authors.forename: E M
authors.initials: EM
authors.lastname: Inack
authors.affiliation: Complex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea-Cameroon.
authors.forename: E M
authors.initials: EM
authors.lastname: Yamakou
mesh_terms: D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D001921:Brain / Q000502:physiology*; D003198:Computer Simulation; D025461:Feedback, Physiological / Q000502:physiology; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D017711:Nonlinear Dynamics; D009435:Synaptic Transmission / Q000502:physiology*