Collective dynamics of periodic nonlinear oscillators under simultaneous parametric and external excitations

The collective dynamics of a periodic structure of coupled Duffing–Van Der Pol oscillators is investigated under simultaneous external and parametric excitations. An analytico-computational model based on a perturbation technique, combined with standing wave decomposition and the asymptotic numerical method is developed for a finite number of coupled oscillators. The frequency responses and the basins of attraction are analyzed for the case of small arrays, demonstrating the importance of the multi-mode solutions and the robustness of their attractors. This model can be exploited to design periodic structure-based smart systems with high performance, by taking advantage of the multi-modes induced by the collective dynamics.