Double Hopf bifurcation in delay differential equations

• DOI: 10.1016/j.ajmsc.2013.10.002
• Publication Date: 2013-11-01T21:40:19Z
• Authors: Redouane Qesmi; Mohamed Ait Babram
• Keywords: Delay differential equation; Center manifold; Pitchfork bifurcation

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