Abstract
A formal perturbation method is derived for the study of bifurcation near a degenerate zero eigenvalue. This results in a third order differential equation with a single quadratic nonlinearity. Numerical solutions of this show successive period doubling bifurcations and eventual “chaos.” The problem arises in the study of neural equations when an additional excitatory channel or cell is added to standard two-component models which oscillate. It also applies to a Van der Pol oscillator coupled to a simple RC circuit. Numerical simulations of a modified FitzHugh–Nagumo system agree qualitatively with the behavior of the bifurcation equations.
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