Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session M45: Focus Session: Emerging Topics in Network Synchronization: Patterns, Stability, and Transitions |
Hide Abstracts |
Chair: Takashi Nishikawa, Northwestern University Room: 216AB |
Wednesday, March 4, 2015 11:15AM - 11:51AM |
M45.00001: Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks Invited Speaker: Louis Pecora Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters in general or understand the conditions for their formation. We show the intimate connection between network symmetry and cluster synchronization. We apply computational group theory to reveal the clusters and determine their stability. In complex networks the symmetries can number in the millions, billions, and more. The connection between symmetry and cluster synchronization is experimentally explored using an electro-optic network. We observe and explain a surprising and common phenomenon (isolated desynchronization) in which some clusters lose synchrony while leaving others connected to them synchronized. We show the isolated desynchronization is intimately related to the decomposition of the group of symmetries into subgroups. The results could guide the design of new power grid systems or lead to new understanding of the dynamical behavior of networks ranging from neural to social. [Preview Abstract] |
Wednesday, March 4, 2015 11:51AM - 12:03PM |
M45.00002: Chimera states: limits and open questions Daniel Abrams, Mark Panaggio ``Chimera states'' are surprising patterns that can be found in systems of identical coupled oscillators, where synchrony and incoherence seem to stably coexist in a spatially asymmetrical state. The existence and stability of chimera states in a variety of settings relevant to real-world systems remains an active topic of research. Here I summarize what is known and present preliminary results for interesting limits including small and large-N, small and large coupling lag, as well as near-local and near-global coupling. [Preview Abstract] |
Wednesday, March 4, 2015 12:03PM - 12:15PM |
M45.00003: Cluster dynamics of pulse coupled oscillators Kevin O'Keeffe, Steven Strogatz, Paul Krapivsky We study the dynamics of networks of pulse coupled oscillators. Much attention has been devoted to the ultimate fate of the system: which conditions lead to a steady state in which all the oscillators are firing synchronously. But little is known about how synchrony builds up from an initially incoherent state. The current work addresses this question. Oscillators start to synchronize by forming clusters of different sizes that fire in unison. First pairs of oscillators, then triplets and so on. These clusters progressively grow by coalescing with others, eventually resulting in the fully synchronized state. We study the mean field model in which the coupling between oscillators is all to all. We use probabilistic arguments to derive a recursive set of evolution equations for these clusters. Using a generating function formalism, we derive simple equations for the moments of these clusters. Our results are in good agreement simulation. We then numerically explore the effects of non-trivial connectivity. Our results have potential application to ultra-low power ``impulse radio'' \& sensor networks. [Preview Abstract] |
Wednesday, March 4, 2015 12:15PM - 12:27PM |
M45.00004: Driven Synchronization in Random Networks of Oscillators Jason Hindes, Christopher R. Myers Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns affect the types of emergent behavior that it can produce. Thus far, modeling efforts have focused on the tendency of networks of oscillators to mutually synchronize themselves, and largely neglected the effects of external driving, even though both effects are present, and often compete, in many naturally occurring systems. In this work we discuss the interplay between mutual and forced synchronization in networks of phase oscillators, and in particular resolve how the structure and emergence of these states depends on the underlying network topology for simple random networks with a given contact distribution. We provide a bifurcation analysis, centering on the unfolding of a Takens-Bogdanov-Cusp singularity, which naturally separates homogeneous and heterogeneous network behavior, and determines the number, stability, and appearance of entrained and mutually synchronized states as a function of a few system parameters. [Preview Abstract] |
Wednesday, March 4, 2015 12:27PM - 12:39PM |
M45.00005: Mode-Locking Behavior of Izhikevich Neuron Under Periodic External Forcing AmirAli Farokhniaee, Edward Large In this study we obtained the regions of existence of various mode-locked states on the periodic-strength plane, which are called Arnold Tongues, for Izhikevich neurons. The study is based on the new model for neurons by Izhikevich (2003) which is the normal form of Hodgkin-Huxley neuron. This model is much simpler in terms of the dimension of the coupled non-linear differential equations compared to other existing models, but excellent for generating the complex spiking patterns observed in real neurons. Many neurons in the auditory system of the brain must encode amplitude variations of a periodic signal. These neurons under periodic stimulation display rich dynamical states including mode-locking and chaotic responses. Periodic stimuli such as sinusoidal waves and amplitude modulated (AM) sounds can lead to various forms of n : m mode-locked states, similar to mode-locking phenomenon in a LASER resonance cavity. Obtaining Arnold tongues provides useful insight into the organization of mode-locking behavior of neurons under periodic forcing. Hence we can describe the construction of harmonic and sub-harmonic responses in the early processing stages of the auditory system, such as the auditory nerve and cochlear nucleus. [Preview Abstract] |
Wednesday, March 4, 2015 12:39PM - 12:51PM |
M45.00006: Synchronization On Hanoi Networks Shanshan Li, Stefan Boettcher Synchronization of coupled oscillators has been intensively studied on a variety of structures. It is believed that the dynamics is deeply associated with its structure. To explore this relation, we study the synchronization of coupled oscillators on Hanoi networks. We analyze the evolution of coupled units over time, and characterized the convergence to the global synchronized state. For this state, the results show a close connection to the spectrum of connectivity matrix. Inspired by this connection, we try to show a dynamical pattern that describes the entire synchronization process from the onset to the final state. This may unveil the unique hierarchical structure of these self-similar Hanoi networks. Our goal is to map the dynamics to the spectrum of the connectivity matrix that encodes significant information about the structure of the underlying system. This exploration may have implications on designing networks that synchronizes coupled units efficiently. [Preview Abstract] |
Wednesday, March 4, 2015 12:51PM - 1:03PM |
M45.00007: Synchronization in growing populations of coupled oscillators and excitable elements Wen Yu, Kevin Wood In biological systems, synchronized dynamics often exist in growing populations. We show here that population growth can have significant effects on collective synchronization in discrete phase models of coupled oscillators or excitable elements. Using numerical simulations, mean field theory, and linear stability analysis, we demonstrate that coupling between population growth and synchrony can lead to a wide range of dynamical behavior, including extinction of synchronized oscillations, the emergence of asynchronous states with unequal state (phase) distributions, bistability between oscillatory and asynchronous states or between two asynchronous states, and modulation of the frequency of bulk oscillations. [Preview Abstract] |
Wednesday, March 4, 2015 1:03PM - 1:15PM |
M45.00008: A Simple Kuramoto-like Circuit Zhuwei Zeng, David Mertens The toy model for spontaneous collective synchronization is the Kuramoto model, a model of nonlinear coupled phase oscillators. Although it is a popular theoretical tool, the Kuramoto model is too simple to accurately characterize the dynamics of any experimental collection of oscillators. In this talk, we present a simple electronic oscillator design similar to the Wien bridge design of Temirbayev et al. Although the oscillator is not strictly modeled by the Kuramoto model, it can be quantitatively modeled by a more generic phase oscillator model. The coefficients governing the oscillator's behavior can be directly extracted from the voltage time series of the oscillator. We find that, in practice, only a handful of coefficients are necessary to quantitatively describe the behavior of the oscillators, making precise theory tractable. [Preview Abstract] |
Wednesday, March 4, 2015 1:15PM - 1:27PM |
M45.00009: A rule for coarse graining phase oscillator models David Mertens The Kuramoto model is often studied as a paradigm for synchronization. Among phase oscillator models, the Kuramoto model exhibits unique properties that simplify the analysis, and call into question whether or not results from the Kuramoto model are applicable to other phase oscillator models. Instead of focusing on the Kuramoto model, I show how a coarse graining procedure can be applied to generic phase oscillator models with global coupling, providing an alternative method for analyzing their critical behavior. In particular, I discuss a simple geometrically motivated rule that is crucial for the coarse graining approximations. [Preview Abstract] |
Wednesday, March 4, 2015 1:27PM - 1:39PM |
M45.00010: Phase patterns in finite oscillator networks with insights from the piecewise linear approximation Daniel Goldstein Recent experiments on spatially extend arrays of droplets containing Belousov-Zhabotinsky reactants have shown a rich variety of spatio-temporal patterns. Motivated by this experimental set up, we study a simple model of chemical oscillators in the highly nonlinear excitable regime in order to gain insight into the mechanism giving rise to the observed multistable attractors. When coupled, these two attractors have different preferred phase synchronizations, leading to complex behavior. We study rings of coupled oscillators and observe a rich array of oscillating patterns. We combine Turing analysis and a piecewise linear approximation to better understand the observed patterns. [Preview Abstract] |
Wednesday, March 4, 2015 1:39PM - 1:51PM |
M45.00011: Improving the Network Structure can lead to Functional Failures Tiago Pereira, Philipp Pade In many real-world networks the ability to synchronize is a key property for their performance. Examples include power-grid, sensor, and neuron networks as well as consensus formation. Recent work on undirected networks with diffusive interaction revealed that improvements in the network connectivity such as making the network more connected and homogeneous enhances synchronization. However, real-world networks have directed and weighted connections. In such directed networks, understanding the impact of structural changes on the network performance remains a major challenge. Here, we show that improving the structure of a directed network can lead to a failure in the network function. For instance, introducing new links to reduce the minimum distance between nodes can lead to instabilities in the synchronized motion. This counter-intuitive effect only occurs in directed networks. Our results allow to identify the dynamical importance of a link and thereby have a major impact on the design and control of directed networks. [Preview Abstract] |
Wednesday, March 4, 2015 1:51PM - 2:03PM |
M45.00012: Observability and Controllability of Nonlinear Networks: The Role of Symmetry Steven Schiff, Andrew Whalen, Sean Brennan, Timothy Sauer Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. For example, noncontrollable mathematical models of real systems may have subspaces that influence model behavior, but cannot be controlled by an input. Such subspaces are difficult to determine in complex nonlinear networks. Since most of the present theory was developed for linear networks without symmetries, here 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 measures of observability and controllability. We numerically observe and theoretically predict that not all symmetries have the same effect on network observation and control. We find that the presence of symmetry in a network may decrease observability and controllability, although networks containing only rotational symmetries remain controllable and observable. These results alter our view of the nature of observability and controllability in complex networks, change our understanding of structural controllability, and affect the design of mathematical models to observe and control such networks. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit 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 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700