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Register a new userChaos synchronization in networks of delay-coupled lasers: Role of the coupling phases
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We derive rigorous conditions for the synchronization of all-optically coupled lasers. In particular, we elucidate the role of the optical coupling phases for synchronizability by systematically discussing all possible network motifs containing two lasers with delayed coupling and feedback. Hereby we explain previous experimental findings. Further, we study larger networks and elaborate optimal conditions for chaos synchronization. We show that the relative phases between lasers can be used to optimize the effective coupling matrix.
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We show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice. We analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent. The zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices and we analytically estimate the synchronization error bounds.
We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties of static and fluctuating networks, we find that random network alternations can enhance the synchronizability. Synchronized states appear to be maximally stable when fluctuations are much faster than the time-delay, even when the instantaneous state of the network does not allow synchronization. This enhancing effect disappears for very slow fluctuations. For fluctuation time scales of the order of the time-delay, a desynchronizing resonance is reported. Moreover, we observe characteristic oscillations, with a periodicity related to the coupling delay, as the system approaches or drifts away from the synchronized state.
We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability approach, we find that the master stability function shows a discrete rotational symmetry depending on the number of groups. The coupling matrices that permit solutions on group or cluster synchronization manifolds show a very similar symmetry in their eigenvalue spectrum, which helps to simplify the evaluation of the master stability function. Our theory allows for the characterization of stability of different patterns of synchronized dynamics in networks with multiple delay times, multiple coupling functions, but also with multiple kinds of local dynamics in the networks nodes. We illustrate our results by calculating stability in the example of delay-coupled semiconductor lasers and in a model for neuronal spiking dynamics.
We theoretically study chaos synchronization of two lasers which are delay-coupled via an active or a passive relay. While the lasers are synchronized, their dynamics is identical to a single laser with delayed feedback for a passive relay and identical to two delay-coupled lasers for an active relay. Depending on the coupling parameters the system exhibits bubbling, i.e., noise-induced desynchronization, or on-off intermittency. We associate the desynchronization dynamics in the coherence collapse and low frequency fluctuation regimes with the transverse instability of some of the compound cavitys antimodes. Finally, we demonstrate how, by using an active relay, bubbling can be suppressed.
Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex networks both analytically and numerically. The temporal variation is rather general and formalized as being driven by a metric dynamical system. Four network models are discussed in detail in which the interconnections between vertices vary through time randomly. These models are 1) i.i.d. sequences of random graphs with fixed wiring probability, 2) groups of graphs with random switches between the individual graphs, 3) graphs with temporary random failures of nodes, and 4) the meet-for-dinner model where the vertices are randomly grouped. We show that the temporal variation and randomness of the connection topology can enhance synchronizability in many cases; however, there are also instances where they reduce synchronizability. In analytical terms, the Hajnal diameter of the coupling matrix sequence is presented as a measure for the synchronizability of the graph topology. In topological terms, the decisive criterion for synchronization of coupled chaotic maps is that the union of the time-varying graphs contains a spanning tree.
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