Prog. Theor. Phys. Vol. 66 No. 1 (1981) pp. 143-153
A Reductive Perturbation Approach to Hard-Mode Instabilities of Inverted-Type Bifurcations
Department of Electronics, Kyushu University, Fukuoka 812
(Received February 4, 1981)
Characteristic behavior of a hard-moed instability near the critical point between normal and inverted bifurcations is discussed by means of a reductive perturbation with respect to a new small parameter. The equation resulting from the fifth order of the present perturbation has a form similar to the usual Time-Dependent-Ginzburg-Landau equation, except for an additional term. For a steady and spatially uniform case, the present equation can describe a variation of the amplitude of self-oscillation as the type of bifurcation varies from normal to inverted ones. In this paper the present approach is applied to the FitzHugh-Nagumo model as a typical example, while it can be used generally for hard-mode instabilities of inverted-type bifurcations near the critical points.
DOI : 10.1143/PTP.66.143
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