Transmission thresholds in time-periodically driven nonlinear disordered systems

Details Transmission thresholds in time-periodically driven nonlinear disordered systems Transmission thresholds in time-periodically driven nonlinear disordered systems

2008-12-18

arxiv.org/abs/0812.3620v2

EPL, 86 (2009) 10009

Nonlinear Sciences

Pattern Formation and Solitons

6 pages, 6 figures, to be published in EPL. Revised version: minor clarifications and updates of references

Scientific paper

10.1209/0295-5075/86/10009

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.

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