Stability of synchronization in dissipatively driven Frenkel-Kontorova models

Abstract

We rigorously show that dissipatively driven Frenkel-Kontorova models with either uniform or time-periodic driving asymptotically synchronize for a wide range of initial conditions. The main tool is a new Lyapunov function, as well as a 2D representation of the attractor. We then characterize dynamical phase transitions and outline new algorithms for determining them.

References in corpus (1)

• Uniform boundedness and long-time asymptotics for the two-dimensional Navier-Stokes equations in an infinite cylinder

Cited by in corpus (1)

• Random Matrix Ensembles in Hyperchaotic Classical Dissipative Dynamical Systems