โ Scribed by Michele Bonnin
No coin nor oath required. For personal study only.
We investigate the existence and the stability of waves and phase locked states in rings of coupled oscillators with delayed interactions. Using center manifold reduction and the normal form method, we reduce the equation governing the dynamics of the whole network to an amplitude-phase model (i.e. a set of coupled ordinary differential equations describing the evolution of both the amplitudes and the phases of the oscillators). Then we prove the existence of traveling waves, in-phase and antiphase locked oscillations, in both one-dimensional and two-dimensional lattices. The influence of the interaction strength and the number of oscillators is investigated, and the possible coexistence of waves and phase locked oscillations is shown.
๐ SIMILAR VOLUMES
Consider an infinite chain of particles subjected to a potential f , where nearest neighbours are connected by nonlinear oscillators. The nonlinear coupling between particles is given by a potential V . The dynamics of the system is described by the infinite system of second order differential equat