Periodization of Duffing oscillators suspended on elastic structure: Mechanical explanation

We consider the dynamics of chaotic oscillators suspended on the elastic structure. We show that for the given conditions of the structure, initially uncorrelated chaotic oscillators can synchronize both in chaotic and periodic regimes. The phenomena of the periodization, i.e., the behavior of nonlinear oscillators become periodic as a result of interaction with elastic structure, have been observed. We formulate the criterion for periodization of double well-potential Duffing oscillator evolution in terms of the forces and displacements in the spring elements. We argue that the observed phenomena are generic in the parameter space and independent of the number of oscillators and their location on the elastic structure.