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An analysis of a dendritic neuron model with an active membrane site. (English) Zbl 0587.92012
Considered is a mathematical model of a coupling between a passive dendrite and an active boundary (axonal or somatic) site. It is represented by a passive cable equation with a nonlinear boundary condition resuming the form of a space-clamped FitzHugh-Nagumo equation (FHNE).
Bifurcation analysis is carried out for the FHNE in the cases of steady and periodic applied current and for the complex model as well, using asymptotic methods. As a result, interesting neuronal phenomena at this coupling site are described.

MSC:
92Cxx Physiological, cellular and medical topics
35B32 Bifurcations in context of PDEs
92C05 Biophysics
35Q99 Partial differential equations of mathematical physics and other areas of application
34C25 Periodic solutions to ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
Software:
AUTO
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