Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session E14: Symmetries, Spatiotemporal Patterns and SynchronizationFocus

Hide Abstracts 
Sponsoring Units: GSNP Chair: Takashia Nishikawa, Northwestern University Room: 273 
Tuesday, March 14, 2017 8:00AM  8:36AM 
E14.00001: Symmetric States Requiring System Asymmetry in Oscillator Networks Invited Speaker: Adilson Motter Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. In this presentation, I will report on our discovery of the converse of symmetry breakingthe scenario in which complete synchronization is not stable for identically coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones. [Preview Abstract] 
Tuesday, March 14, 2017 8:36AM  8:48AM 
E14.00002: Symmetries and stability of chimera states in small, globallycoupled networks Joseph D. Hart, Kanika Bansal, Thomas E. Murphy, Rajarshi Roy It has recently been demonstrated that symmetries in a network's topology can help predict the patterns of synchronized clusters that can emerge in a network of coupled oscillators. This and related discoveries have led to increased interest in both network symmetries and cluster synchronization.~ In parallel with these discoveries, interest in chimera statesdynamical patterns in which a network separates into coherent and incoherent portionshas grown, and chimeras have now been observed in a variety of experimental systems. We present an optoelectronic experiment in which both chimera states and synchronized clusters are observed in a small, globallycoupled network. We show that the symmetries and subsymmetries of the network permit the formation of the chimera and cluster states. A recently developed group theoretical approach enables us to predict the stability of the observed chimera and cluster states, and highlights the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization. [Preview Abstract] 
Tuesday, March 14, 2017 8:48AM  9:00AM 
E14.00003: Experimental observation of spiral wave chimeras in coupled chemical oscillators Jan Totz, Kenneth Showalter, Harald Engel I will present a versatile setup based on optically coupled catalytic microparticles, that allows for the experimental study of synchronization patterns in very large networks of relaxation oscillators under wellcontrolled laboratory conditions. In particular I will show our experimental observation of the spiral wave chimera, predicted by Kuramoto in 2003. This pattern features a wave rotating around a spatially extended core that consists of phaserandomized oscillators. We study its existence depending on coupling parameters and observe a transition to incoherence via core growth and splitting. The spiral wave chimera is likely to play a role in cardiac and cortical cell ensembles, as well as in cilia carpets. [Preview Abstract] 
Tuesday, March 14, 2017 9:00AM  9:12AM 
E14.00004: Chimera states in 1 and 2 dimensions in a 5$^{\mathrm{th}}$ order FitzHughNagumo model Andrea Welsh, Flavio Fenton The FitzHughNagumo model is a simple, two variables model used as a quantitative description of the dynamical behavior of an excitable neuron and of other excitable systems. This model uses one variable to mimic the membrane potential and a second variable for recovery of excitability and has become a central example in reactiondiffusion systems. Typical solutions for this model are stable oscillations or excitations depending on parameters. By converting the 3rd order reaction term to a 5th order, we are able to induce oscillations or excitation states depending only on initial conditions. In this talk we present first results of this new system with chimera states, the coexistence of coherence and incoherence which are already studied in coupled oscillator systems, in one dimensional cables and rings, and in two dimensional grids representing tissues. [Preview Abstract] 
Tuesday, March 14, 2017 9:12AM  9:24AM 
E14.00005: Control of traveling localized spots Steffen Martens, Jakob Löber, Harald Engel, Christopher Ryll, Fredi Tröltzsch Besides traveling waves, moving localized spots represent yet another important class of selforganized spatiotemporal structures in nonequilibrium dissipative systems. In this talk, we present two different approaches to guide localized spots along a pregiven trajectory. First, an analytical solution for the control  being an openloop control  is proposed which attempts to shift the spot's ``center of mass'' according to a given protocol of movement without disturbing its profile [J.~L{\"o}ber and H.~Engel, PRL \textbf{112}, 148305; J.~L{\"o}ber, PRE \textbf{89}, 62904]. The control signal is expressed in terms of the uncontrolled spot profile and its propagation velocity; rendering detailed informations about the reaction kinetics unnecessary. Secondly, optimal control with Tikhonov regularization is used. Noteworthy, both control schemes coincide for vanishing regularization term. In particular, our analytic control is an excellent initial guess for the numerical solution of optimal control problems; thereby achieving a substantial computational speedup [C. Ryll et al., \textit{Control of SelfOrganizing Nonlinear Systems} (Springer, BerlinHeidelberg, 2016)]. [Preview Abstract] 
Tuesday, March 14, 2017 9:24AM  9:36AM 
E14.00006: Synchronization in Random Pulse Oscillator Networks Kevin Brown, Ann Hermundstad Motivated by synchronization phenomena in neural systems, we study synchronization of random networks of coupled pulse oscillators. We begin by considering binomial random networks whose nodes have intrinsic linear dynamics. We quantify order in the network spiking dynamics using a new measure: the normalized LevZimpel complexity (LZC) of the nodes' spike trains. Starting from a globallysynchronized state, we see two broad classes of behaviors. In one ("temporally random"), the LZC is high and nodes spike independently with no coherent pattern. In another ("temporally regular"), the network does not globally synchronize but instead forms coherent, repeating population firing patterns with low LZC. No topological feature of the network reliably predicts whether an individual network will show temporally random or regular behavior; however, we find evidence that degree heterogeneity in binomial networks has a strong effect on the resulting state. To confirm these findings, we generate random networks with independentlyadjustable degree mean and variance. We find that the likelihood of temporallyrandom behavior increases as degree variance increases. Our results indicate the subtle and complex relationship between network structure and dynamics. [Preview Abstract] 
Tuesday, March 14, 2017 9:36AM  10:12AM 
E14.00007: Experimental Network Dynamics: Symmetries and Synchronization Patterns Invited Speaker: Rajarshi Roy There are many challenges for experimental scientists to explore in the field of network dynamics, not the least of which is to find suitable platforms for quantitative observations to test new ideas and concepts in this rapidly evolving field. Three central challenges are (a) How does one gather data efficiently and precisely from the networks small and large to investigate aspects that do not merely confirm predictions from numerical simulations? (b) Can we design experimental systems with their heterogeneities and noise sources well enough to test predictions from idealized models and yet reveal unanticipated surprises? (c) How do we interweave theory, numerical simulations and experiments so that they complement each other and lead us to deeper understanding of the basic principles of network dynamics and motivate us to develop new applications? We describe how experimenters and theoreticians can interact to advance our understanding of the effects of symmetries on network dynamics. Experiments which probe the existence and stability of synchronization patterns that reveal themselves in experiments and connect concepts from group theory, stability analysis and test the numerical modeling of deterministic and stochastic systems will be used to illustrate these ideas. [Preview Abstract] 
Tuesday, March 14, 2017 10:12AM  10:24AM 
E14.00008: Optimizing Synchronization Stability of the Kuramoto Model in Complex Networks and Power Grids Bo Li, K. Y. Michael Wong Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. For the Kuramoto model on general weighted networks, the synchronization stability, measured by the dominant Lyapunov exponent at the steady state, is shown to have intricate and nonlinear dependence on the network topology and the dynamical parameters. Specifically, the dominant Lyapunov exponent corresponds to the algebraic connectivity of a metagraph whose edge weight depends nonlinearly on the steady states. In this study, we utilize the cutset space (DC) approximation to estimate the nonlinear steady state and simplify the calculation of the stability measure, based on which we further derive efficient algorithms to optimize the synchronization stability. The properties of the optimized networks and application in power grid stability are also discussed. [Preview Abstract] 
Tuesday, March 14, 2017 10:24AM  10:36AM 
E14.00009: Improving synchronization via local rewiring in networks of Kuramoto oscillators Lia Papadopoulos, Jason Kim, Danielle Bassett Synchronization of nonidentical oscillators coupled through complex networks is an important example of collective behavior, and many studies examine how the architecture of interactions shapes synchronization patterns. Here, we focus on adaptive networks, where the structure of the underlying network changes in response to the node dynamics. In particular, we use the Kuramoto model to investigate how via a local rewiring rule, an initially random network converges to a topology that supports improved synchronization. The adaptation strategy preserves the total number of edges, and depends only on instantaneous, pairwise phase differences of neighboring nodes. In the case of binary, undirected networks, a local rule that preserves connections between more desynchronized oscillators, and that breaks and rewires connections between more in phase oscillators, can improve synchronization. Furthermore, in line with results from studies on optimal synchronization, throughout adaptation the Laplacian spectra and the relationship between its eigenvectors and the intrinsic frequencies undergo specific changes. Finally, we find that after sufficient adaptation, the resulting network exhibits degree  frequency and frequency  neighbor frequency correlations that have been associated with explosive synchronization transitions. By considering the interplay between structure and dynamics, this work helps elucidate a mechanism through which emergent phenomena can arise in complex systems. [Preview Abstract] 
Tuesday, March 14, 2017 10:36AM  10:48AM 
E14.00010: Model of photoinduced structural change induced by THz pulse irradiation Kunio Ishida, Keiichiro Nasu Recently intense optical pulses with THz frequency have been obtained, and it is of interest to study the effect of irradiated THz pulses on electronic systems. We theoretically study the photoinduced cooperative dynamics triggered by irradiation of THz pulses. We employed a model of twolevel localized electrons coupled with an optical phonon mode taking into account the nonadiabaticity of the electron dynamics, and solved the timedependent Schr\"odinger equation numerically. We consider the cases in which the THz pulses create phonons near the surface of the system, and pursue the electronic transitions induced by the propagation of the phonons. We found that they are able to induce excitedstate domain growth, and that the interference between them plays an important role in the growth dynamics. Hence, the domain growth is affected by the geometry of the surface of the system, which is different from the photoinduced structural change by visible/UV pulses. We also show that the nonadiabatic/adiabatic electronic transitions should be taken into account though the domain growth mainly proceeds on the groundstate potential energy surfaces(PESs). In other words, the energy level/structure of excitedstate PESs are relevant to the domaingrowth dynamics. [Preview Abstract] 
Tuesday, March 14, 2017 10:48AM  11:00AM 
E14.00011: Selforganized criticality with synchrony and selfbreaking phenomena Jongha Jeon, Pilwon Kim Selforganizing and spontaneous breaking are seemingly opposite phenomena, and hardly captured in a single model. We develop a second order Kuramoto model \footnote{F. D orfler and F. Bullo, \textit{On the critical coupling for Kuramoto oscillators} , May. 2011. Available at https://arxiv.org/pdf/1011.3878 .} \footnote{Y.P. Choi, S.Y. Ha, and S.B. Yun, \textit{Complete synchronization of Kuramoto oscillators with finite inertia}, Physica D, {\bf 240}, 3244 (2011)} with relative damping(friction) which shows frequency locking together with spontaneous synchrony breaking. As the oscillators are synchronizing in frequency, the relative friction decreases accordingly, eventually making the system marginally stable. In the regime that the interacting force and the damping ratio are of same order, the dynamic behaviors of the oscillators alternate irregularly through the process between synchronization, formationbreaking, and reorganization. Especially when the oscillators are maintaining frequency locking, the system’s reaction against a random external perturbation shows a powerlaw distribution, which is another evidence of selforganized criticality\footnote{Steven H. Strogatz. \textit{Exploring complex networks}, Nature {\bf410}, 268276 (2001).} inherited in the system [Preview Abstract] 
Follow Us 
Engage
Become an APS Member 
My APS
Renew Membership 
Information for 
About APSThe American Physical Society (APS) is a nonprofit membership organization working to advance the knowledge of physics. 
© 2020 American Physical Society
 All rights reserved  Terms of Use
 Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 207403844
(301) 2093200
Editorial Office
1 Research Road, Ridge, NY 119612701
(631) 5914000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 200452001
(202) 6628700