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DY: Fachverband Dynamik und Statistische Physik

DY 10: Posters I

DY 10.32: Poster

Montag, 14. März 2011, 17:00–19:00, P4

Master stability function for time-delayed networks of chaotic semiconductor lasers — •Sven Heiligenthal, Anja Englert, Marco Winkler, and Wolfgang Kinzel — Julius-Maximilians-University, Würzburg, Germany

The master stability function allows to calculate the stability of the synchronization manifold of arbitrary networks. We use this method to numerically analyze the stability of several different networks of chaotic semiconductor lasers with time-delayed mutual couplings by simulating the Lang-Kobayashi equations.

We make predictions about the synchronizability of such networks by relating the modulus of the second largest eigenvalue of the network's adjacency matrix to the maximal Lyapunov exponent of the network dynamics. Our numerical simulations confirm these predictions for two examples of different network topologies.

Furthermore, we show symmetries of the master stability function for networks with two different delay times which were recently proven for networks of simple Bernoulli maps. Our numerical results for networks of chaotic semiconductor lasers show these symmetries, as well.

Finally, we show by using the master stability function that networks of chaotic semiconductor lasers in which the delay time of the mutual couplings is much larger than the internal time scales of the chaotic lasers cannot be synchronized if the local Lyapunov exponent is positive. We also make a proposal for an experimental method which can measure this local Lyapunov exponent.