Report

Synchronized Chaos in Coupled Optical Feedback Networks Briana E. Mork, Gustavus Adolphus College Katherine R. Coppess, University of Michigan Natural dynamical system: Chaos; order and randomness Oscillators (Nodes) Synchrony http://2.bp.blogspot.com/-73jjFxeZhjc/TIRe264OII/AAAAAAAADXU/2PBDgyH2Ufk/s400/Brain_Highways.png Kitzbichler (2009) PLoS Comput Biol 5(3) Man-made dynamical system: Periodic (mostly) Oscillators (Nodes) Synchrony http://www.efoodsdirect.com/blog/wp-content/uploads/2013/10/power-grid-drill.jpg Examples of Four-Node Network Topologies Experimental Four-Node Network Topologies Summer 2014 Previously studied CRS Williams et al. CHAOS 23, 043117 (2013) The Experiment CRS Williams et al. CHAOS 23, 043117 (2013) Four nodes form a delay-coupled system with weighted and directed links. Weight is determined by the coupling strength ε as implemented by the DSP board. Dynamics of a Node Changing the feedback strength β of a node varies the dynamics of the node. CRS Williams et al. CHAOS 23, 043117 (2013) time (ms) Experimental Network Topologies Bidirectional ring Bidirectional chain with unidirectional links Bottom: Laplacian coupling matrices for the two networks, respectively. Bidirectional Ring Bidirectional Ring Bidirectional Chain with Unidirectional Links Conclusions - The synchronous states that arise depend on topology of the network. - Transitions between synchronous states depend on coupling strength. Future work - Stability analysis for synchronous states - Many-node networks - Comparison of convergence rates between global and cluster synchrony Acknowledgments Caitlin R. S. Williams, Washington and Lee University Aaron M. Hagerstrom, University of Maryland Louis Pecora, Naval Research Laboratory Francesco Sorrentino, University of New Mexico Thomas E. Murphy, University of Maryland Rajarshi Roy, University of Maryland For More Information... Synchronization states and multistability in a ring of periodic oscillators: Experimentally variable coupling delays CRS Williams et al. CHAOS 23, 043117 (2013) Experimental Observations of Group Synchrony in a System of Chaotic Optoelectronic Oscillators CRS Williams et al. PRL 110, 064104 (2013) Cluster Synchronization and Isolated Desynchronization in Complex Networks with Symmetries L Pecora et al. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5079 (2014)