Transmission thresholds in time-periodically driven nonlinear disordered systemsM. Johansson1, 2, G. Kopidakis3, 2, S. Lepri4, 2 and S. Aubry5, 2
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
received 5 December 2008; accepted in final form 16 March 2009; published April 2009
published online 22 April 2009
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.
05.45.-a - Nonlinear dynamics and chaos.
05.60.-k - Transport processes.
42.25.Dd - Wave propagation in random media.
© EPLA 2009