Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session C56: Networks of Oscillators |
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Sponsoring Units: GSNP Chair: Daniel Lathrop, University of Maryland, College Park Room: BCEC 255 |
Monday, March 4, 2019 2:30PM - 2:42PM |
C56.00001: Synchronous Clustering in Multilayered Networks Louis Pecora, Karen Blaha, Ke Huang, Fabio Della Rossa, Mani Hossein-Zadeh, Abu Bakar Siddique, Francesco Sorrentino The topic of cluster synchronization of oscillators in networks has an active history and has recently experienced renewed interest in the nonlinear dynamics community because of the use of such graph theory tools as symmetries and equitable partitions to predict what cluster structures are possible, calculate their dynamic stability, and characterize their bifurcations as they desynchronize. Another recent network structure that has caught the interest of the dynamics community is multilayered networks. We show how to extend the graph theory tools to multilayered networks. Certain multilayered networks have a structure that allows their dynamics to be simplified and fit into the existing structure of analysis of synchronous clusters. We also present a recent experiment on a simple 4-oscillator multilayer system. We show what can be discerned from experimental data including bifurcation plots and desynchronization patterns. This is the first experiment on cluster synchronization that we know of that uses totally analog oscillators with no computer-aided control of the oscillators. We also will discuss how some of the concepts can be generalized. |
Monday, March 4, 2019 2:42PM - 2:54PM |
C56.00002: Spontaneous data clustering using collective synchronization in a network of phase oscillators Takaya Miyano, Shinya Takaramoto We developed a method for spontaneous data clustering based on Kuramoto’s model for collective synchronization. A network of phase oscillators, to the natural frequencies of which multivariate data are input, achieves partial synchrony owing to short range interaction between neighboring phase oscillators. The common frequencies of the partial synchronous groups represent major feature patterns of the multivariate data. As a case study, we apply our method to actually observed time series of wind velocity and show major feature patterns of the wind data. |
Monday, March 4, 2019 2:54PM - 3:06PM |
C56.00003: Interdependent and competitive dynamics in multilayer networks: synchronization and epidemics Michael Danziger, Ivan Bonamassa, Stefano Boccaletti, Shlomo Havlin Since 2010, research on interdependent networks of networks, has demonstrated relevant new percolation phenomena including cascading failures and abrupt discontinuous transitions [1, 2]. However, this approach is limited to cases where connectivity can be taken as a proxy for functionality. Here, we present new research on interacting network dynamics exhibiting a wide range of new phenomena which are observed in the real-world but absent in previous models. By extending the concept of connectivity and dependency links to dynamical processes, we are able to shed light on real-world complex systems from social networks to the brain. We demonstrate our approach by implementing interdependent and competitive synchronization based on the Kuramoto model [3, 4] and SIS epidemics. This new framework provides a key missing link in the modeling of real-world multilayer networks. The talk is based on our recent manuscript [5]. |
Monday, March 4, 2019 3:06PM - 3:18PM |
C56.00004: Synchronization of chaotic oscillators using partial state space linear control KEYUR MISTRY, Sudeshna Dash, Siddharth Tallur The idea of synchronization of chaotic oscillators traces its origin to pioneering work by T. L. Carroll and L. M. Pecora in the late 1980s. Numerous implementations reported over the last three decades either require all state variables of a master oscillator to generate a locking signal to entrain the slave oscillators, or use a subset of the state variables, albeit with nonlinear transfer function. We present a novel methodology in which locking signal is generated as i) a linear combination of ii) a partial subset of state variables of the oscillators. The unused state variables can be exploited for applications in cryptography. A generalized algorithm for controller design is presented, and the efficacy of this algorithm is proved by analyzing the piece-wise oscillator as multi-mode linear system. Root-locus method is used to compute feedback gain. Simplicity of the control system makes it possible to reliably realize all-analog, all-digital, or mixed-signal implementations for electronic oscillators, with low power and cost overheads. The methodology is validated through numerical simulations and experiments using op-amp based electronic circuits. |
Monday, March 4, 2019 3:18PM - 3:30PM |
C56.00005: Almost Perfect In-Phase and Anti-Phase Chaotic and Periodic Phase Synchronization in Large Arrays of Diode Lasers Yehuda Braiman, Niketh Nair, Erik Bochove We studied phase synchronization in large arrays of weakly coupled single mode semiconductor laser diodes [1,2]. We show that if the coupling topology is chosen appropriately, the laser array exhibits robust and almost perfect phase synchrony (including chaotic and non-chaotic phase synchrony). Furthermore, one can define coupling topologies that lead to chaotic anti-phase synchronization. When diodes are coupled via a decayed non-local coupling scheme, the leading spatial mode can be stable. This leads to an almost-perfect phase synchronous state where the phases are synchronized, even though the system is not being exactly on the synchronization manifold. This almost-perfect phase synchronous state is robust to noise and frequency and phase disorder and can be realized under periodic (fixed-intensity limit cycle) continuous-wave and chaotic behavior. |
Monday, March 4, 2019 3:30PM - 3:42PM |
C56.00006: Global Frequency Locking of Networks of Coherently Coupled Lasers Jiajie Ding, Mohammad-Ali Miri Nonlinear dynamics of networks of coupled oscillators is a subject of great interest in various disciplines ranging from electrical circuits and chemical reactions to biological cells and social systems. A universal property of such networks is a self-organized oscillation at a common frequency, which is often referred to as synchronization. Here, we investigate the frequency locking of a network of coupled lasers. In this regard, we introduce a first-order nonlinear coupled-mode model for optical oscillators representing semiconductor lasers. We show that two coupled oscillators with different individual frequencies can be synchronized in frequency when the mutual coupling rate exceeds a critical level. The threshold coupling is calculated and explored in the parameter space of the system. Next, we investigate synchronization in one- and two-dimensional arrays of lasers with uniform nearest neighbor coupling and explore the synchronization threshold as a function of the size of the network. Finally, we discuss that a more complex network topology is required in order to enforce global synchronization in a large network of coupled lasers. |
Monday, March 4, 2019 3:42PM - 3:54PM |
C56.00007: Optimal fluctuation pathways to desynchronization in coupled oscillator networks Jason Hindes There is great interest in understanding how topology, dynamics, and uncertainty conspire to produce rare and extreme events in networks. This is particularly the case for coupled oscillator networks since they appear at the core of many biological and physical systems where noise and uncertainty play a significant role. A primary example is desynchronization in power grids from input-power fluctuations. In this talk, we develop theory for the most-likely, or optimal, pathway of noise-induced desynchronization in phase-oscillator networks (with and without inertia) and in Stuart-Landau oscillator networks. We quantitatively characterize the scalings and patterns for the optimal path and the probability of desynchronization as a function of network topology and local dynamics, and compare the behavior for the various models. Lastly, we discuss the effects of non-Gaussian, “pulse” noise, and controls on the input power, on desynchronization. Such effects are especially relevant for power grids with renewable energy sources. |
Monday, March 4, 2019 3:54PM - 4:06PM |
C56.00008: Control of a Multistable 3-ring Network of Chemical Oscillators Christopher Simonetti, Michael Norton, Maria Eleni Moustaka, Seth Fraden The Belousov-Zhabotinsky reaction is a limit cycle oscillator with dynamical attributes comparable to neurons. By fabricating microfluidic wells filled with the BZ chemistry, we create reaction-diffusion networks with rich dynamical patterns that can yield fundamental insights into dynamics of neural networks. A simple network of three inhibitor-coupled wells connected in a ring possesses two stable, dynamical steady states: clockwise and counterclockwise traveling waves. By photo-chemically perturbing the wells’ intrinsic frequencies we can force the system to switch states. In this work, we explore the steady states as a function of applied light gradient using the Kuramoto phase model and Vanaag-Epstein model for photosensitive BZ. Optimal control theory is then applied to determine the most efficient way to drive the system from one attractor to another. |
Monday, March 4, 2019 4:06PM - 4:18PM |
C56.00009: Features of a rich attractor space in a system of repulsively coupled Kuramoto oscillators Shadisadat Esmaeili, Darka Labavic, Hildegard Meyer-Ortmanns, Michel Pleimling Rhythmic behaviors with a wide range of periods emerge from populations of coupled oscillators in many phenomena in nature. The Kuramoto model is one of the simplest models of coupled oscillators vastly used to explain many such phenomena. Choosing a repulsive coupling and a proper topology in this model leads to frustration and, as a result, versatile features of multistability. Also, by choosing non-homogeneous natural frequencies, in a large enough system orbits emerge with very long periods that are orders of magnitude longer than the natural frequencies. To understand the characteristics of the phase space we study the effects of tuning parameters like the coupling constant and the width of the frequency distribution. |
Monday, March 4, 2019 4:18PM - 4:30PM |
C56.00010: Overcoming oscillation quenching in coupled nonlinear oscillators Nannan Zhao, Zhongkui Sun Rhythmic oscillation activity plays an important role in various natural and artificial systems. However, the appearance of oscillation quenching phenomena can lead to a loss or degradation of intrinsic function for many practical systems. In this work, we introduce a simple method based on the external positive feedback that can efficiently revoke these quenching states in different coupling schemes. Taking the limit cycle Stuart-Landau systems as example, we have illustrated numerically and analytically that tuning the feedback strength can shrinks drastically the oscillation quenching regions in the parameter space. Our study will provide a new and general framework to retrieve the rhythmicity or the strengthen the robustness for dynamic activity of coupled nonlinear systems. |
Monday, March 4, 2019 4:30PM - 4:42PM |
C56.00011: Effects of variation of coupling offset α in electronic oscillator experiments MacMillan Wheeler, Taylor GurrEithun, Shelby Stegmaier, David Mertens In biological systems that exhibit synchronization, oscillators within a single population vary in many aspects. To provide controlled experimental insight into how these variations affect synchronization, we have built an ensemble of highly configurable electronic oscillators. These oscillators have programmable speed, coupling strength, waveform shape, and coupling phase offset, known as α in the Sakaguchi-Kuramoto model. Moreover, each oscillator can have a distinct coupling offset. We have examined how α affects the degree of synchronization, and how variations in α within a population alter the stability of the synchronous state. We will also compare our findings with those presented in the literature. |
Monday, March 4, 2019 4:42PM - 4:54PM |
C56.00012: Relaxation oscillators, limit cycle oscillators, and somewhere in between: experimental exploration of waveform variation in synchronizing oscillators Taylor GurrEithun, MacMillan Wheeler, Shelby Stegmaier, David Mertens In biological systems that exhibit synchronization, oscillators within a single population vary not only in their natural rates, but in many other characteristics. To study such variations experimentally, we have built an ensemble of highly configurable electronic oscillators. These oscillators have programmable speed, coupling strength, coupling phase offset, and waveform. Each oscillator's waveform can be tuned from approximately sinusoidal to relaxational, effectively altering the interaction from a nearly sinusoidal one to a more complex form. To our knowledge, interactions between oscillators with different waveforms have not been examined. In this talk, we will present our findings on how variations in waveform in a single population affect the system's ability to synchronize. |
Monday, March 4, 2019 4:54PM - 5:06PM |
C56.00013: Dynamics of the Kuramoto-Sakaguchi Oscillator Network with Asymmetric Order Parameter Jan Engelbrecht, Bolun Chen, Renato Mirollo Kuramoto oscillator networks are an important idealized class of oscillator models. We consider a generalized network in which the order parameter is the sum of the complex oscillator phases, but with non-identical coefficients. We analyze this model using a dimensional reduction from dynamics on an N-dimensional state space to a flow on the unit disk, where the natural hyperbolic metric facilitates the analysis. We give a fairly complete classification of the asymptotic dynamics with careful consideration of the subtleties of the flow near the disk's boundary, which includes both fully synchronized states and (N-1,1) states where all but one of the oscillators are synchronized. The geometric connection also allows us to identify conditions for the flows to be gradient, or Hamiltonian or even simultaneously gradient and Hamiltonian. Examples of new behavior in the asymmetric model include, (N-1,1) attractors with a basin of non-zero measure and homoclinic and heteroclinic non-periodic orbits to/from sync and (N−1,1) states in the Hamiltonian case. |
Monday, March 4, 2019 5:06PM - 5:18PM |
C56.00014: Double-Period Breathers in a Driven-Damped Lattice Golan Bel, Boian S Alexandrov, Alan Reginald Bishop, Kim Ø Rasmussen Spatially localized and temporally oscillating solutions, known as discrete breathers, have been experimentally and theoretically discovered in many physical systems. We considered a lattice of coupled damped and driven Helmholtz-Duffing oscillators in which we found a spatial coexistence of oscillating solutions with different frequencies. Specifically, we demonstrated that stable period-doubled solutions coexist with solutions oscillating at the frequency of the driving force. Such solution represents period-doubled breathers resulting from a stability overlap between subharmonic and harmonic solutions and exist up to a certain strength of the lattice coupling. Our findings suggest that this phenomenon can occur in any driven lattice where the nonlinearity admits bistability (or multi-stability) of subharmonic and harmonic solutions. |
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