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Paulino Monroy Castillero, Arik Yochelis
A generic mechanism for the emergence of spatially localized states embedded in an oscillatory background is demonstrated by using a 2:1 frequency locking oscillatory system. The localization is of Turing type and appears in two space dimensions as a comb-like state in either π phase shifted Hopf oscillations or inside a spiral core. Specifically, the localized states appear in absence of the well known flip-flop dynamics (associated with collapsed homoclinic snaking) that is known to arise in the vicinity of Hopf-Turing bifurcation in one space dimension...
April 2017: Chaos
Daniel Weingard, Wilfredo Blanco, Oliver Steinbock, Richard Bertram
In three-dimensional reaction-diffusion systems, excitation waves may form and rotate around a one-dimensional phase singularity called the filament. If the filament forms a closed curve, it will shrink over time and eventually collapse. However, filaments may pin to non-reactive objects present in the medium, reducing their rate of collapse or even allowing them to persist indefinitely. We use numerical simulations to study how different arrangements of non-reactive spheres affect the dynamics of circular filaments...
April 2017: Chaos
Bo Li, David Saad
Chimera-like states are manifested through the coexistence of synchronous and asynchronous dynamics and have been observed in various systems. To analyze the role of network topology in giving rise to chimera-like states, we study a heterogeneous network model comprising two groups of nodes, of high and low degrees of connectivity. The architecture facilitates the analysis of the system, which separates into a densely connected coherent group of nodes, perturbed by their sparsely connected drifting neighbors...
April 2017: Chaos
Carl P Dettmann, Vitaly Fain
An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk...
April 2017: Chaos
David Papo, Joaquin Goñi, Javier M Buldú
No abstract text is available yet for this article.
April 2017: Chaos
Rémi Delage, Yusuke Takayama, Tetsushi Biwa
This paper documents on-off intermittency observed in coupled thermoacoustic chaotic oscillations. Mode competition between two or three oscillation modes engenders chaotic oscillations through quasiperiodic oscillations introduced by a local cross-sectional change in a gas-filled tube. Complete synchronization is then obtained by connecting two thermoacoustic chaotic oscillators via a rigid plate with an orifice. From the analysis of pressure fluctuations, theoretical statistical scaling laws related to the laminar phases, spectral density, and amplitude probability distribution are found to be satisfied in the coupled thermoacoustic oscillators, when the thermoacoustic complete synchronization breaks down through an on-off intermittency route with the decreased orifice size...
April 2017: Chaos
Karlis Kanders, Tom Lorimer, Ruedi Stoop
There are indications that for optimizing neural computation, neural networks may operate at criticality. Previous approaches have used distinct fingerprints of criticality, leaving open the question whether the different notions would necessarily reflect different aspects of one and the same instance of criticality, or whether they could potentially refer to distinct instances of criticality. In this work, we choose avalanche criticality and edge-of-chaos criticality and demonstrate for a recurrent spiking neural network that avalanche criticality does not necessarily entrain dynamical edge-of-chaos criticality...
April 2017: Chaos
Hai-Qiong Zhao, Guo-Fu Yu
In this paper, a spatial discrete complex modified Korteweg-de Vries equation is investigated. The Lax pair, conservation laws, Darboux transformations, and breather and rational wave solutions to the semi-discrete system are presented. The distinguished feature of the model is that the discrete rational solution can possess new W-shape rational periodic-solitary waves that were not reported before. In addition, the first-order rogue waves reach peak amplitudes which are at least three times of the background amplitude, whereas their continuous counterparts are exactly three times the constant background...
April 2017: Chaos
Wen-Rong Sun, De-Yin Liu, Xi-Yang Xie
We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrödinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics...
April 2017: Chaos
Sarab S Sethi, Valerio Zerbi, Nicole Wenderoth, Alex Fornito, Ben D Fulcher
Brain dynamics are thought to unfold on a network determined by the pattern of axonal connections linking pairs of neuronal elements; the so-called connectome. Prior work has indicated that structural brain connectivity constrains pairwise correlations of brain dynamics ("functional connectivity"), but it is not known whether inter-regional axonal connectivity is related to the intrinsic dynamics of individual brain areas. Here we investigate this relationship using a weighted, directed mesoscale mouse connectome from the Allen Mouse Brain Connectivity Atlas and resting state functional MRI (rs-fMRI) time-series data measured in 184 brain regions in eighteen anesthetized mice...
April 2017: Chaos
Víctor J López-Madrona, Fernanda S Matias, Ernesto Pereda, Santiago Canals, Claudio R Mirasso
Inferring effective connectivity from neurophysiological data is a challenging task. In particular, only a finite (and usually small) number of sites are simultaneously recorded, while the response of one of these sites can be influenced by other sites that are not being recorded. In the hippocampal formation, for instance, the connections between areas CA1-CA3, the dentate gyrus (DG), and the entorhinal cortex (EC) are well established. However, little is known about the relations within the EC layers, which might strongly affect the resulting effective connectivity estimations...
April 2017: Chaos
Aradhana Singh, Sarika Jalan, Stefano Boccaletti
Communication delays and multiplexing are ubiquitous features of real-world network systems. We here introduce a simple model where these two features are simultaneously present and report the rich phenomenology which is actually due to their interplay on cluster synchronization. A delay in one layer has non trivial impacts on the collective dynamics of the other layers, enhancing or suppressing synchronization. At the same time, multiplexing may also enhance cluster synchronization of delayed layers. We elucidate several nontrivial (and anti-intuitive) scenarios, which are of interest and potential application in various real-world systems, where the introduction of a delay may render synchronization of a layer robust against changes in the properties of the other layers...
April 2017: Chaos
Zhixin Lu, Jaideep Pathak, Brian Hunt, Michelle Girvan, Roger Brockett, Edward Ott
Deducing the state of a dynamical system as a function of time from a limited number of concurrent system state measurements is an important problem of great practical utility. A scheme that accomplishes this is called an "observer." We consider the case in which a model of the system is unavailable or insufficiently accurate, but "training" time series data of the desired state variables are available for a short period of time, and a limited number of other system variables are continually measured. We propose a solution to this problem using networks of neuron-like units known as "reservoir computers...
April 2017: Chaos
Jasmeet Singh, Rahul Belur Vishwanath, Swetaprovo Chaudhuri, R I Sujith
In this paper, a generalized description of the complex topology of turbulent premixed flames stabilized in a model gas turbine combustor is obtained using network analysis. Networks are created using the visibility algorithm applied to points on the flame edge obtained from Hydroxyl radical (OH)-Planar Laser Induced Fluorescence images of turbulent premixed flames. The network structure thus obtained showed the emergence of a few massively connected nodes which were found to represent the folded regions of the flame front...
April 2017: Chaos
Bernadette J Stolz, Heather A Harrington, Mason A Porter
We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results. Our first example uses time-series output from networks of coupled Kuramoto oscillators. Our second example consists of biological data in the form of functional magnetic resonance imaging data that were acquired from human subjects during a simple motor-learning task in which subjects were monitored for three days during a five-day period...
April 2017: Chaos
Fabrizio Damicelli, Claus C Hilgetag, Marc-Thorsten Hütt, Arnaud Messé
Topological features play a major role in the emergence of complex brain network dynamics underlying brain function. Specific topological properties of brain networks, such as their modular organization, have been widely studied in recent years and shown to be ubiquitous across spatial scales and species. However, the mechanisms underlying the generation and maintenance of such features are still unclear. Using a minimalistic network model with excitable nodes and discrete deterministic dynamics, we studied the effects of a local Hebbian plasticity rule on global network topology...
April 2017: Chaos
Lachlan D Smith, Murray Rudman, Daniel R Lester, Guy Metcalfe
Understanding the mechanisms that control three-dimensional (3D) fluid transport is central to many processes, including mixing, chemical reaction, and biological activity. Here a novel mechanism for 3D transport is uncovered where fluid particles are kicked between streamlines near a localized shear, which occurs in many flows and materials. This results in 3D transport similar to Resonance Induced Dispersion (RID); however, this new mechanism is more rapid and mutually incompatible with RID. We explore its governing impact with both an abstract 2-action flow and a model fluid flow...
April 2017: Chaos
Thomas D Nevins, Douglas H Kelley
We present an algorithm for measuring the speed and thickness of reaction fronts, and from those quantities, the diffusivity and the reaction rate of the active chemical species. This front-tracking algorithm provides local measurements suitable for statistics and requires only a sequence of concentration fields. Though our eventual goal is front tracking in advection-reaction-diffusion, here we demonstrate the algorithm in reaction-diffusion. We test the algorithm with validation data in which front speed and thickness are prescribed, as well as simulation results in which diffusivity and reaction rate are prescribed...
April 2017: Chaos
Lucas Campanari, Min Ju You, Peter Langfield, Leon Glass, Alvin Shrier
Experiments were carried out in monolayer tissue cultures of embryonic chick heart cells imaged using a calcium sensitive fluorescent dye. The cells were grown in annular geometries and in annular geometries with an isthmus connecting antipodal region of the annulus. We observed a large number of spatially different patterns of propagation consisting of one or more circulating waves. As well, we also observed rhythms in which rotors embedded in the annuli generated propagating pulses. These results demonstrate that many different patterns of excitation can be present in cardiac tissue with simple geometries...
April 2017: Chaos
Christian Geier, Klaus Lehnertz
We investigate the temporal and spatial variability of the importance of brain regions in evolving epileptic brain networks. We construct these networks from multiday, multichannel electroencephalographic data recorded from 17 epilepsy patients and use centrality indices to assess the importance of brain regions. Time-resolved indications of highest importance fluctuate over time to a greater or lesser extent, however, with some periodic temporal structure that can mostly be attributed to phenomena unrelated to the disease...
April 2017: Chaos
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