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Olga I Moskalenko, Nikita S Frolov, Alexey A Koronovskii, Alexander E Hramov
In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems...
December 2017: Chaos
Jeffrey B Weiss, Ian Grooms
Mesoscale eddies are one of the dominant sources of variability in the world's oceans. With eddy-resolving global ocean models, it becomes important to assimilate observations of mesoscale eddies to correctly represent the state of the mesoscale. Here, we investigate strategies for assimilating a reduced number of sea-surface height observations by focusing on the coherent mesoscale eddies. The study is carried out in an idealized perfect-model framework using two-layer forced quasigeostrophic dynamics, which captures the dominant dynamics of ocean mesoscale eddies...
December 2017: Chaos
Henry D I Abarbanel, Sasha Shirman, Daniel Breen, Nirag Kadakia, Daniel Rey, Eve Armstrong, Daniel Margoliash
Networks of nonlinear systems contain unknown parameters and dynamical degrees of freedom that may not be observable with existing instruments. From observable state variables, we want to estimate the connectivity of a model of such a network and determine the full state of the model at the termination of a temporal observation window during which measurements transfer information to a model of the network. The model state at the termination of a measurement window acts as an initial condition for predicting the future behavior of the network...
December 2017: Chaos
Ben P Kirtman, Natalie Perlin, Leo Siqueira
A suite of coupled climate model simulations and experiments are used to examine how resolved mesoscale ocean features affect aspects of climate variability, air-sea interactions, and predictability. In combination with control simulations, experiments with the interactive ensemble coupling strategy are used to further amplify the role of the oceanic mesoscale field and the associated air-sea feedbacks and predictability. The basic intent of the interactive ensemble coupling strategy is to reduce the atmospheric noise at the air-sea interface, allowing an assessment of how noise affects the variability, and in this case, it is also used to diagnose predictability from the perspective of signal-to-noise ratios...
December 2017: Chaos
Kirsten Stahn, Klaus Lehnertz
We aim at identifying factors that may affect the characteristics of evolving weighted networks derived from empirical observations. To this end, we employ various chains of analysis that are often used in field studies for a data-driven derivation and characterization of such networks. As an example, we consider fully connected, weighted functional brain networks before, during, and after epileptic seizures that we derive from multichannel electroencephalographic data recorded from epilepsy patients. For these evolving networks, we estimate clustering coefficient and average shortest path length in a time-resolved manner...
December 2017: Chaos
Xuelian Cui, Narisa Zhao
Social networks are rarely static, and they typically have time-varying network topologies. A great number of studies have modeled temporal networks and explored social contagion processes within these models; however, few of these studies have considered community structure variations. In this paper, we present a study of how the time-varying property of a modular structure influences the information dissemination. First, we propose a continuous-time Markov model of information diffusion where two parameters, mobility rate and community attractiveness, are introduced to address the time-varying nature of the community structure...
December 2017: Chaos
Jinge Wang, Jeffrey Tithof, Thomas D Nevins, Rony O Colón, Douglas H Kelley
We experimentally study spreading of the Belousov-Zhabotinsky reaction behind a bluff body in a laminar flow. Locations of reacted regions (i.e., regions with high product concentration) correlate with a moderate range of Lagrangian stretching and that range is close to the range of optimal stretching previously observed in topologically different flows [T. D. Nevins and D. H. Kelley, Phys. Rev. Lett. 117, 164502 (2016)]. The previous work found optimal stretching in a closed, vortex dominated flow, but this article uses an open flow and only a small area of appreciable vorticity...
December 2017: Chaos
Evelyn Hamilton, Nicolas Bruot, Pietro Cicuta
The chimera state is the incongruous situation where coherent and incoherent populations coexist in sets of identical oscillators. Using driven non-linear oscillators interacting purely through hydrodynamic forces at low Reynolds number, previously studied as a simple model of motile cilia supporting waves, we find concurrent incoherent and synchronised subsets in small arrays. The chimeras seen in simulation display a "breathing" aspect, reminiscent of uniformly interacting phase oscillators. In contrast to other systems where chimera has been observed, this system has a well-defined interaction metric, and we know that the emergent dynamics inherit the symmetry of the underlying Oseen tensor eigenmodes...
December 2017: Chaos
Stephen G Penny
The state-of-the-art data assimilation methods used today in operational weather prediction centers around the world can be classified as generalized one-way coupled impulsive synchronization. This classification permits the investigation of hybrid data assimilation methods, which combine dynamic error estimates of the system state with long time-averaged (climatological) error estimates, from a synchronization perspective. Illustrative results show how dynamically informed formulations of the coupling matrix (via an Ensemble Kalman Filter, EnKF) can lead to synchronization when observing networks are sparse and how hybrid methods can lead to synchronization when those dynamic formulations are inadequate (due to small ensemble sizes)...
December 2017: Chaos
Friethjof Theel, Antonia Karamatskou, Robin Santra
The Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the Hartree-Fock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals...
December 2017: Chaos
Nataliya Stankevich, Erik Mosekilde
Classification of the dynamical mechanisms that support bistability between bursting oscillations and silence has not yet been clarified in detail. The purpose of this paper is to demonstrate that the coexistence of a stable equilibrium point with a state of continuous bursting can occur in a slightly modified, biophysical model that describe the dynamics of pancreatic beta-cells. To realize this form of coexistence, we have introduced an additional voltage-dependent potassium current that is activated in the region around the original, unstable equilibrium point...
December 2017: Chaos
Joseph D Hart, Don C Schmadel, Thomas E Murphy, Rajarshi Roy
We report a new experimental approach using an optoelectronic feedback loop to investigate the dynamics of oscillators coupled on large complex networks with arbitrary topology. Our implementation is based on a single optoelectronic feedback loop with time delays. We use the space-time interpretation of systems with time delay to create large networks of coupled maps. Others have performed similar experiments using high-pass filters to implement the coupling; this restricts the network topology to the coupling of only a few nearest neighbors...
December 2017: Chaos
W Wiegerinck, F M Selten
Recently, supermodels consisting of an ensemble of interacting models, synchronizing on a common solution, have been proposed as an alternative to the common non-interactive multi-model ensembles in order to improve climate predictions. The connection terms in the interacting ensemble are to be optimized based on the data. The supermodel approach has been successfully demonstrated in a number of simulation experiments with an assumed ground truth and a set of good, but imperfect models. The supermodels were optimized with respect to their short-term prediction error...
December 2017: Chaos
Gregory S Duane, Carsten Grabow, Frank Selten, Michael Ghil
The synchronization of loosely coupled chaotic systems has increasingly found applications to large networks of differential equations and to models of continuous media. These applications are at the core of the present Focus Issue. Synchronization between a system and its model, based on limited observations, gives a new perspective on data assimilation. Synchronization among different models of the same system defines a supermodel that can achieve partial consensus among models that otherwise disagree in several respects...
December 2017: Chaos
Debraj Nath, Yali Gao, R Babu Mareeswaran, T Kanna, Barnana Roy
We explore different nonlinear coherent structures, namely, bright-dark (BD) and dark-dark (DD) solitons in a coupled nonlinear Schrödinger/Gross-Pitaevskii equation with defocusing/repulsive nonlinearity coefficients featuring parity-time ( PT)-symmetric potentials. Especially, for two choices of PT-symmetric potentials, we obtain the exact solutions for BD and DD solitons. We perform the linear stability analysis of the obtained coherent structures. The results of this linear stability analysis are well corroborated by direct numerical simulation incorporating small random noise...
December 2017: Chaos
Steffen O P Blume, Giovanni Sansavini
Complex dynamical systems face abrupt transitions into unstable and catastrophic regimes. These critical transitions are triggered by gradual modifications in stressors, which push the dynamical system towards unstable regimes. Bifurcation analysis can characterize such critical thresholds, beyond which systems become unstable. Moreover, the stochasticity of the external stressors causes small-scale fluctuations in the system response. In some systems, the decomposition of these signal fluctuations into precursor signals can reveal early warning signs prior to the critical transition...
December 2017: Chaos
Jaideep Pathak, Zhixin Lu, Brian R Hunt, Michelle Girvan, Edward Ott
We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal...
December 2017: Chaos
Chenggui Yao, Meng Zhan, Jianwei Shuai, Jun Ma, Jürgen Kurths
It has been generally believed that both time delay and network structure could play a crucial role in determining collective dynamical behaviors in complex systems. In this work, we study the influence of coupling strength, time delay, and network topology on synchronization behavior in delay-coupled networks of chaotic pendulums. Interestingly, we find that the threshold value of the coupling strength for complete synchronization in such networks strongly depends on the time delay in the coupling, but appears to be insensitive to the network structure...
December 2017: Chaos
Tianyu Yuan, Gouhei Tanaka
Robustness of coupled oscillator networks against local degradation of oscillators has been intensively studied in this decade. The oscillation behavior on the whole network is typically reduced with an increase in the fraction of degraded (inactive) oscillators. The critical fraction of inactive oscillators, at which a transition from an oscillatory to a quiescent state occurs, has been used as a measure for the network robustness. The larger (smaller) this measure is, the more robust (fragile) the oscillatory behavior on the network is...
December 2017: Chaos
Sabine Auer, Frank Hellmann, Marie Krause, Jürgen Kurths
90% of all Renewable Energy Power in Germany is installed in tree-like distribution grids. Intermittent power fluctuations from such sources introduce new dynamics into the lower grid layers. At the same time, distributed resources will have to contribute to stabilize the grid against these fluctuations in the future. In this paper, we model a system of distributed resources as oscillators on a tree-like, lossy power grid and its ability to withstand desynchronization from localized intermittent renewable infeed...
December 2017: Chaos
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