Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system

摘要

We consider a class of three-dimensional systems having an equilibrium point at the ori- gin, whose principal part is of the form (-partial derivative h/partial derivative y(x, y), partial derivative x(x,y), f(x,y))(T). This principal part, which has zero divergence and does not depend on the third variable z, is the coupling of a planar Hamiltonian vector field X-h(x,X-y): = (-partial derivative h/partial derivative y(x, y), partial derivative x(x,y))(T) with a one-dimensional system.