Synchronization phenomena in the system consisting of \(m\) coupled Berger plates (Q2480342)

In the present study the author deals with the problem of nonlinear oscillations of an arbitrary number \(m\) of coupled plates. The main goal of this work is the study of the long-time behaviour of the trajectories of the problem under consideration. He obtains results for the case when the coupling operator \(K\) is nonnegative and degenerate. Under these assumptions the author states the existence of the global attractor of the dynamical system, generated by the problem, for all nonnegative values of coupling parameter \(\gamma\). The author proves that the attractor is continuous in the Hausdorff metric with respect to \(\gamma\). He shows that, when \(\gamma\to\infty\) it converges upper semicontinuously to the attractor of the system, generated by the projection of the vector field of the coupled system on the kernel of the coupling operator \(K\). In particular, the author treats the case of 3-diagonal coupling matrix in details. The case of cluster synchronization is considered as well.