Double Hopf bifurcation in delay differential equations

Abstract

The paper addresses the computation of elements of double Hopf bifurcation for retarded functional differential equations (FDEs) with parameters. We present an efficient method for computing, simultaneously, the coefficients of center manifolds and normal forms, in terms of the original FDEs, associated with the double Hopf singularity up to an arbitrary order. Finally, we apply our results to a nonlinear model with periodic delay. This shows the applicability of the methodology in the study of delay models arising in either natural or technological problems.

Keywords

• Double Hopf
• Delay
• Bifurcation
• Functional differential equation
• Center manifold
• Normal forms
• Regenerative cutting tool