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2004•International Journal of Bifurcation and ChaosOpen access

A DESIGN METHOD OF BURSTING USING TWO-PARAMETER BIFURCATION DIAGRAMS IN FITZHUGH–NAGUMO MODEL

Shigeki Tsuji, Tetsushi Ueta, Hiroshi Kawakami, Kazuyuki Aihara

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Abstract

Spiking and bursting observed in nerve membranes seem to be important when we investigate information representation model in the brain. Many topologically different bursting responses are observed in the mathematical models and their related bifurcation mechanisms have been clarified. In this paper, we propose a design method to generate bursting responses in FitzHugh–Nagumo model with a simple periodic external force based on bifurcation analysis. Some effective parameter perturbations for the amplitude of the external input are given from the two-parameter bifurcation diagram.

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What this paper is about

Spiking and bursting observed in nerve membranes seem to be important when we investigate information representation model in the brain. Many topologically different bursting responses are observed in the mathematical models and their related bifurcation mechanisms have been clarified. In this paper, we propose a design method to generate bursting responses in FitzHugh–Nagumo model with a simple periodic external force based on bifurcation analysis. Some effective parameter perturbations for the amplitude of the external input are given from the two-parameter bifurcation diagram.

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Available abstract

Spiking and bursting observed in nerve membranes seem to be important when we investigate information representation model in the brain. Many topologically different bursting responses are observed in the mathematical models and their related bifurcation mechanisms have been clarified. In this paper, we propose a design method to generate bursting responses in FitzHugh–Nagumo model with a simple periodic external force based on bifurcation analysis. Some effective parameter perturbations for the amplitude of the external input are given from the two-parameter bifurcation diagram.

Key concepts: Bursting, Bifurcation, Bifurcation diagram, Representation (politics), Biological applications of bifurcation theory, Amplitude, Saddle-node bifurcation, Control theory (sociology)

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