title: Bifurcation analysis of the travelling waveform of FitzHugh-Nagumo nerve conduction model equation.
abstract: The FitzHugh-Nagumo model for travelling wave type neuron excitation is studied in detail. Carrying out a linear stability analysis near the equilibrium point, we bring out various interesting bifurcations which the system admits when a specific Z(2) symmetry is present and when it is not. Based on a center manifold reduction and normal form analysis, the Hopf normal form is deduced. The condition for the onset of limit cycle oscillations is found to agree well with the numerical results. We further demonstrate numerically that the system admits a period doubling route to chaos both in the presence as well as in the absence of constant external stimuli. (c) 1997 American Institute of Physics.
authors.affiliation: Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli 620 024, India.
authors.forename: P.
authors.initials: P
authors.lastname: Muruganandam
authors.forename: M.
authors.initials: M
authors.lastname: Lakshmanan