Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities

الملخص EN

An efficient method is proposed to study delay-induced strong resonant double Hopf bifurcation for nonlinear systems with time delay.

As an illustration, the proposed method is employed to investigate the 1 : 2 double Hopf bifurcation in the van der Pol system with time delay.

Dynamics arising from the bifurcation are classified qualitatively and expressed approximately in a closed form for either square or cubic nonlinearity.

The results show that 1 : 2 resonance can lead to codimension-three and codimension-two bifurcations.

The validity of analytical predictions is shown by their consistency with numerical simulations.