Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator

Abstract EN

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling.

Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours.

A two-time scales method is used to obtain the frequency-amplitude modulation.

The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator.

The stability of the dynamic motions is also analyzed.

The coupled system shows a hysteretic response pattern and symmetry-breaking facets.

Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.