SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 18: Nonlinear Dynamics, Synchronization and Chaos

DY 18.6: Vortrag

Dienstag, 28. März 2023, 11:30–11:45, ZEU 148

Manifolds of equilibrium states in ensembles of globally coupled oscillators — •Michael Zaks — Humboldt Universität zu Berlin, Berlin, Germany

Global fields generated by ensembles of coupled oscillators are responsible for many unusual kinds of collective behavior. Among their most striking effects are existence of numerous constants of motion and a drastic reduction in the number of degrees of freedom. Here, we offer a simpler approach, restricted to the widespread situations in which the number of parameters defining the action of the global fields is smaller than the overall number of elements in the ensemble. In the phase space of such ensembles, high-dimensional manifolds composed of the equilibrium states can generically arise. Existence of these manifolds is not related to symmetries. In the simplest cases, such continua of steady states are attracting or repelling as a whole; in general, however, their stability with respect to transversal perturbations varies in the course of the motion along the manifold. Remarkably, the suggested mechanism does not require that all oscillators are identical: the sufficiently strong global field is able to counteract diversity among the ensemble units and halt the temporal evolution.