Berlin 2012 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 6: Delay Dynamics
DY 6.5: Vortrag
Montag, 26. März 2012, 16:00–16:15, MA 144
Strong and Weak Chaos in Nonlinear Networks with Time-Delayed Couplings — •Sven Heiligenthal1, Thomas Dahms2, Serhiy Yanchuk3, Thomas Jüngling1, Valentin Flunkert2, Ido Kanter4, Eckehard Schöll2, and Wolfgang Kinzel1 — 1University of Würzburg, Würzburg, Germany — 2Technical University of Berlin, Berlin, Germany — 3Humboldt University of Berlin, Berlin, Germany — 4Bar-Ilan University, Ramat-Gan, Israel
We investigate networks of nonlinear units with time-delayed couplings in the limit of large delay times. We find two kinds of chaos which we call strong and weak. For strong chaos the largest Lyapunov exponent (LE) is of the order of the inverse time scales of the individual units. For weak chaos the largest LE is of the order of the inverse delay time. As a consequence, networks with strong chaos cannot synchronize, whereas for weak chaos, networks can synchronize if the product of the largest LE and the delay time is sufficiently small compared to the eigenvalue gap of the coupling matrix. We can prove that the occurrence of strong and weak chaos is determined by the sign of the instantaneous LE. For semiconductor lasers, numerical simulations of the Lang-Kobayashi equations predict that by monotonically increasing the strength of the time-delayed coupling or feedback, the chaos changes from weak to strong and back to weak chaos. We suggest an experimental setup to measure the difference between strong and weak chaos, which we have realized in an experiment with two coupled electronic circuits.
See also: S. Heiligenthal et al., Phys. Rev. Lett. 107, 234102 (2011).