Transmission thresholds in time-periodically driven nonlinear disordered systems

¹  Department of Physics, Chemistry and Biology (IFM), Linköping University - SE-581 83 Linköping, Sweden, EU
²  Max Planck Institute for the Physics of Complex Systems - Nöthnitzer Str. 38, D-01187 Dresden, Germany, EU
³  Department of Materials Science and Technology, University of Crete - GR-71003 Heraklion, Greece, EU
⁴  Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche - via Madonna del piano 10, I-50019 Sesto Fiorentino, Italy, EU
⁵  Laboratoire Léon Brillouin, CEA Saclay - 91191 Gif-sur-Yvette, France, EU

Corresponding author: majoh@ifm.liu.se

Received: 5 December 2008
Accepted: 16 March 2009

Abstract

We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) below threshold, localized quasiperiodic oscillations and no spreading; 2) three different regimes in time close to threshold, with almost regular oscillations initially, weak chaos and slow spreading for intermediate times and finally strong diffusion; 3) immediate spreading for strong driving. The thresholds are due to simple bifurcations, obtained analytically for a single oscillator, and numerically as turning points of the nonlinear response manifold for a full chain. Generically, the threshold is nonzero also for infinite chains.