Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session F40: Patterns of Network SynchronizationInvited

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Sponsoring Units: GSNP Chair: Adilson Motter, Northwestern University Room: 387 
Tuesday, March 14, 2017 11:15AM  11:51AM 
F40.00001: Using Symmetries and Equitable Partitions Together to Find All Synchronization Clusters and Their Stability Invited Speaker: Louis Pecora Many networks of coupled oscillators are observed to produce patterns of synchronized clusters where all the oscillators in each cluster have exactly the same dynamical trajectories in state space, but not the same as oscillators in other clusters. It has been difficult to predict these clusters in general. We show the intimate connection between network symmetry and cluster synchronization. We apply computational group theory to reveal the clusters and determine their stability. Other synchronization clusters are possible in addition to the symmetry clusters (SC). These are equitable partitions (EP) of the network. We show that the EP can be constructed by the merging of appropriate SC. We show that this construction also allows the derivation of further simplified stability (variational) equations for the EP case thus allowing the SC and EP approaches to compliment each other. The connection between symmetry and cluster synchronization is experimentally explored using an electrooptic network. [Preview Abstract] 
Tuesday, March 14, 2017 11:51AM  12:27PM 
F40.00002: Prevalence of AsymmetryInduced Synchronization in Oscillator Networks Invited Speaker: Takashi Nishikawa A counterintuitive scenario has recently been discovered in which, in order to stabilize complete synchrony of all oscillatorsa symmetric statein a symmetric network, the oscillators must become nonidentical and thus break the system symmetry. This phenomenon, which is termed asymmetryinduced symmetry (AIS) and can be regarded as the converse of symmetry breaking, calls for a systematic investigation into how often such behavior is observed in complex systems. In this talk, I will present a general scheme for constructing AIS systems and demonstrate that AIS is the norm rather than exception in coupled oscillator networks that can be viewed as multilayer networks. In this construction, oscillator heterogeneity stems from the heterogeneity of interlayer connections, and the master stability function formalism is used to establish synchronization stability properties. Since a network in complete synchrony is the basic building block of more general complex networks with clusters of synchronous oscillators, our results suggest the prevalence of networks in which observing synchrony in a cluster requires that the cluster break its symmetry, and thus have implications beyond the class of fully symmetric networks. [Preview Abstract] 
Tuesday, March 14, 2017 12:27PM  1:03PM 
F40.00003: Observability and Controllability of Networks: Symmetry in Representations of Brains and Controllers for Epidemics Invited Speaker: Steven Schiff Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. We present a numerical and group representational framework, to quantify the observability and controllability of nonlinear networks with explicit symmetries that shows the connection between symmetries and nonlinear measures of observability and controllability. In addition to the topology of brain networks, we have advanced our ability to represent network nodes within the brain using conservation principles and more accurate biophysics that unifies the dynamics of spikes, seizures, and spreading depression. Lastly, we show how symmetries in controller design can be applied to infectious disease epidemics. [Preview Abstract] 
Tuesday, March 14, 2017 1:03PM  1:39PM 
F40.00004: Control of coupled oscillator networks with application to microgrid technologies Invited Speaker: Alex Arenas The control of complex systems and networkcoupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactionsa paradigmatic example that has guided our understanding of selforganization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable syn chronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself. [Preview Abstract] 
Tuesday, March 14, 2017 1:39PM  2:15PM 
F40.00005: Partially synchronized states in small networks of electrochemical oscillators: effect of heterogeneities and network topology Invited Speaker: Istvan Kiss When electrochemical reactions take place on electrode arrays, a network can form through the potential drop among the elements. Such networks can generate spatially organized partially synchronized states using oscillatory chemical reactions with two fundamental mechanisms. In oscillations with nearly identical natural frequencies, we describe the emergence of chimera states. The experiments point out the importance of low level of heterogeneities (e.g., surface conditions) and optimal level of coupling strength and timescale as necessary components for the realization of the chimera state. For experimental conditions where chimera states are not possible, we analyze the spatially organized partially synchronized states as a function of underlying heterogeneities and network topologies. As a prototype system, we consider three oscillators with superimposed local and global coupling topologies. An analytical formula is derived for the mixed local/global coupling topology for the critical coupling strength at which full synchrony is achieved. The formula is verified with experiments using electrochemical oscillator networks. [Preview Abstract] 
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