COMPARING THE BIFURCATION OF PERIODIC SOLUTIONS FOR GENERIC DIFFERENTIAL EQUATIONS

In this context, equivariant differential equations under the action of certain finite groups are of interest. The solution operator of a system of NFDEs is not a compact operator and does not smooth the initial data as time proceeds, in contrast to delayed functional differential equations. The essential spectrum of the Poincare operator plays a role in establishing the stability of a periodic solution alongside the point spectrum. We demonstrate that the essential spectrum of a periodic solution may undergo a 'normal' bifurcation, altering the solution's stability when it crosses the unit circle.