Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session V47: Dynamical Pattern Formation in Synchronization of Complex NetworksFocus
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Sponsoring Units: GSNP DBIO Chair: Jie Sun, Clarkson Univ Room: LACC 507 |
Thursday, March 8, 2018 2:30PM - 3:06PM |
V47.00001: Unexpected Patterns: Chimera States on Networks Invited Speaker: Daniel Abrams When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. I’ll show evidence for the existence of alternative persistent states that break the symmetries of the underlying coupling network. These symmetry-broken coexistent states are analogous to those dubbed "chimera states," which can occur when identical oscillators are coupled to one another in identical ways. |
Thursday, March 8, 2018 3:06PM - 3:18PM |
V47.00002: Tiered synchronization to traveling-wave state through a metastable state Byungnam Kahng, Jinha Park A first-order phase transition often occurs through a metastable state in diverse systems. However, in synchronization transitions (STs), existence of such a metastable state has been rarely focused up to now, even though its effect will be intriguing. Here we consider a Kuramoto model with two competing types of oscillators which exhibits a hybrid ST. We find that the system stays at the metastable state for a long time to reach a synchronized traveling-wave state. In the metastable state, the order parameter shows large temporal and sample-to-sample fluctuations as in k-core percolation and the number of clusters having similar velocities discretely increases dynamically as in the consciousness recovery process in the human brain. |
Thursday, March 8, 2018 3:18PM - 3:30PM |
V47.00003: Perturbation of Synchronized States via in situ Control of Individual Nodes and Edges Matthew Matheny, Warren Fon, Michael Cross, Michael Roukes Understanding the dynamics of complex networks can be challenging due to the large number of variables that must be tracked. Substantial amounts of data processing is typically required to find correlations between the system degrees-of-freedom in order to intuit information flow. This is the case when the symmetry of the system breaks, as it implies that the network cannot be reduced to a single degree-of-freedom, e.g. the in-phase synchronized state of coupled phase oscillators. In a complex network, simultaneous perturbation of individual or multiple nodes/edges could be an important tool in the understanding of global state behavior. We demonstrate such a tool by probing the dynamics of symmetry broken synchronized states in a ring of 8 coupled nanomechanical oscillators. By employing individual edge and node control we reveal the nature of these broken symmetries. |
Thursday, March 8, 2018 3:30PM - 3:42PM |
V47.00004: Pacemakers versus synchronization in excitable chemical systems Harold Hastings, Maisha Zahed, Sofia Rafikova The Belousov-Zhabotinsky (BZ) chemical reaction is the prototype excitable chemical reaction, a relaxation oscillator consisting of a fast activator (HBrO2) and an inhibitor (Br-) whose production is determined by slow catalytic oxidation of brominated malonic acid. The unstirred BZ reaction in "2D" systems shows a variety of patterns: target patterns generated by oscillatory pacemakers, oscillatory pacemakers in an oscillatory medium, bulk oscillations (synchronized or phase waves), depending upon the catalyst (ferroin, manganese, cerium, mixtures). We describe an experimental and theoretical study of this phenomenon. The type of pattern can be explained, at least in part, by a combination of the redox potential of the catalyst, and the relative time scales of HBrO2 and Br- production. Transitions between dynamical states may help understand "dynamical disease" (see L. Glass, Chaos, 2015) in biological systems. |
Thursday, March 8, 2018 3:42PM - 3:54PM |
V47.00005: Detecting Spatial Defects in Colored Patterns with Coupled Self-Oscillating Gels Yan Fang, Victor Yashin, Samuel Dickerson, Anna Balazs
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Thursday, March 8, 2018 3:54PM - 4:30PM |
V47.00006: Patterns of synchronization, broken symmetries, and attractor switching in a ring of nanoelectromechanical oscillators Invited Speaker: Raissa D'Souza Here we study both theoretically and experimentally an 8-node ring network of coupled nanoelectromechanical (NEMS) oscillators. These are phase and amplitude oscillators driven with a Duffing-type nonlinearity. In addition to typical phase-locked states, we observe synchronized states which break the symmetry of the oscillator ring, including states that have not been discovered previously. We demonstrate that with individual node and edge control within our system, we are able to perturb these states to unveil the nature of these broken symmetries. Finally, we observe the real-time dynamics of of all phase and amplitude degrees-of-freedom and the switching behavior between different steady-state patterns of synchronization. Our experiment demonstrates the promise of coupled NEMS oscillator systems to study open questions in the dynamics and control of complex networks. |
Thursday, March 8, 2018 4:30PM - 4:42PM |
V47.00007: Phase Synchronization and Mode Selection in Arrays of Delay-Coupled Semiconductor Lasers Niketh Nair, Erik Bochove, Yehuda Braiman We consider existence and stability of spatial modes of the external cavity of the delay-coupled semiconductor laser diode array and show that such arrays can be almost perfectly phase synchronized when the cavity is designed appropriately. Using an extension of Master Stability Function theory, we show that by using a decayed nonlocal coupling scheme, it is possible to induce robust and close-to-perfect CW and chaotic phase synchronous states. These synchronous states are robust to noise and moderate amounts of frequency disorder between elements. We also find that the critical coupling strength for which the synchronous state destabilizes increases approximately linearly with array size. |
Thursday, March 8, 2018 4:42PM - 4:54PM |
V47.00008: Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells Alexandra Tayar, Eyal Karzbrun, Vincent Noireaux, Roy Bar-Ziv Understanding how biochemical networks lead to large-scale non- equilibrium self-organization and pattern formation in life is a major challenge, with important implications for the design of programma- ble synthetic systems. Here, we assembled cell-free genetic oscillators in a spatially distributed system of on-chip DNA compartments as artificial cells, and measured reaction–diffusion dynamics at the single- cell level up to the multicell scale. Using a cell-free gene network we programmed molecular interactions that control the frequency of os- cillations, population variability, and dynamical stability. We observed frequency entrainment, synchronized oscillatory reactions and pattern formation in space, as manifestation of collective behavior. The tran- sition to synchrony occurs as the local coupling between compart- ments strengthens. Spatiotemporal oscillations are induced either by a concentration gradient of a diffusible signal, or by spontaneous symmetry breaking close to a transition from oscillatory to nonoscillatory dynamics. |
Thursday, March 8, 2018 4:54PM - 5:06PM |
V47.00009: Geometry and conformal invariants of Kuramoto Oscillator Networks, relating finite N and continuum descriptions Jan Engelbrecht, Renato Mirollo Kuramoto oscillators governed by the same ODE advance in time under the same 3-parameter Möbius transformation. So the dynamics of a state of N identical Kuramoto oscillators is constrained to its G–orbit under the Möbius group action, which is a 3D manifold in TN. The N – 3 independent cross-ratio's of the oscillator phases (eiθj , j = 1, ..., N) are invariants of conformal Möbius transformations. For phase models one can project to 2D orbits and then the oscillator dynamics map to flows on the Poincaré disk. The geometric implications of this correspondence was studied in Ref 1. Here we consider the continuum limit. Previous work identified Poisson densities as the continuum limit of states on the finite N splay orbit. We extend this identification to more complicated densities for which the dynamics preserve new conformal invariants that have a geometric interpretation. Finally we consider continuum networks with distributions of natural frequencies and identify models for which the asymptotic collective order-parameter dynamics correspond to those on the Ott-Antonsen manifold as well as models for which they do not. |
Thursday, March 8, 2018 5:06PM - 5:18PM |
V47.00010: Predicting Finite Size Effects in the Kuramoto Model David Mertens Synchronization is a key phenomenon of coupled nonlinear oscillators. The phase transition evident in many oscillator models has been thoroughly studied in the Kuramoto model, in large part because the order parameter can be obtained analytically for a number of infinite-sized distributions. Nearly all schemes for predicting the order parameter only apply to specific distributions and infinite populations. Schemes for finite populations are rarer and have focused on more tightly prescribed distributions. Finite size effects are essentially uncharacterized. In this talk I will discuss finite size effects in the Kuramoto model. I will begin by illustrating that subsets of oscillators form coherent clumps. For a given population and coupling strength these clumps are reproducible, but they vary widely from one population to the next. Approximations based on the existence and structure of these subsets leads to population specific predictions for subset composition. From these, one can obtain predictions for the average order parameter and its deviation as a function of coupling strength. The predictions exhibit qualitative agreement for a range of distributions, with statistically significant agreement for certain population sizes and coupling strengths. |
Thursday, March 8, 2018 5:18PM - 5:30PM |
V47.00011: Controlling Complex Network Dynamics Through Designer Band Gaps Aden Forrow, Francis Woodhouse, Jorn Dunkel Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such systems, the spectrum of the underlying graph Laplacian plays a key role in controlling the matter or information flow. Traditionally, network theory has focused on analyzing the spectral properties of graph ensembles with predefined statistical adjacency characteristics. Here, we introduce a complementary framework, providing a mathematically rigorous graph construction that exactly realizes any desired spectrum. We illustrate the broad applicability of this approach by showing how designer band gaps can be used to control the dynamics of various archetypal physical systems. Specifically, we demonstrate that a strategically placed gap induces chimera states in Kuramoto-type oscillator networks, completely suppresses pattern formation in a generic Swift-Hohenberg model, and leads to persistent localization in a discrete Gross-Pitaevskii quantum network. This suggests a path to novel band-gapped classes of transport systems, biomimetic networks, or disordered mechanical, optical and acoustic metamaterials. |
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