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Showing 1 to 20 of 34 for “"Kuramoto"”.
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Inherent Instabilities and Discontinuities: The Kuramoto-Sivashinsky Equation and a Suspension Flow as Exemplars
… instability present at small times in the Kuramoto Sivashinsky equation, formulated as a perturbation of the kinematic-wave equation. This instability is invisible to regular matched asymptotic expansions, which, at small times, see no deviation in the leading-order solution from the …
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Application of Uncertainty Inequalities to Bound the Radius of the Attractor for the Kuramoto -Sivashinsky Equation
Made available in DSpace on 2015-09-28T15:19:58Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3250245.pdf: 2544352 bytes, checksum: 11ab9c7e28e1b2b45fc82c5713d9e645 (MD5) Previous issue date: 2006
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Population-specific predictions for the finite Kuramoto model and collective synchronization in a system with resonant coupling
… of distinct auto-oscillators is due to Kuramoto. The most striking feature of the model is the presence of a phase transition from an unsynchronized to a partially synchronized state at a critical value of the inter-oscillator coupling. Also, in spite of being a microscopic model that …
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Synchronization of oscillatory networks in terms of global variables
… of the problem was pioneered by Winfree and Kuramoto. Such a setup gives a possibility for the analysis of these systems in terms of global variables. In this work we describe nontrivial collective dynamics in oscillator populations coupled via mean fields in terms of global variables. We …
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Dynamical systems on networks
… results for two distinct dynamical models: the Kuramoto model, a general model for coupled oscillator systems, and a model for opinion formation in social networks. Our main focus is on understanding the fixed points of these systems and their stability. For many models the stability of such …
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Contributions to mixing and hypocoercivity in kinetic models
… to both the Vlasov–Poisson equation and the Kuramoto equation. These kinetic models come from very different areas of physics: the Vlasov–Poisson equation models plasmas and the Kuramoto equation models synchronisation behaviour. The stability was first described by Landau in 1946 and is a …
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Pattern formation through synchronization in systems of nonidentical autonomous oscillators
… extensive computer simulations. We use the Kuramoto model which reduces general oscillatory systems to phase dynamics. The symmetry of the coupling plays an important role for the formation of patterns. We have studied the ordering influence of an asymmetry (non-isochronicity) in the phase …
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Clustering Behavior in Systems of Coupled Oscillators and Networks of Mutually Attracting Agents
… model voor gekoppelde oscillatoren (het Kuramoto-model) bestudeerd, en worden een aantal analytische resultaten afgeleid met betrekking tot het optreden van gesynchroniseerde groepen, en dit zowel voor systemen met een eindig aantal oscillatoren als voor systemen met een oneindig aantal …
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Dynamics on networks
… by a single network. We first consider the Kuramoto model, a canonical model of coupled phase oscillators. We obtain two results on its partial phase-locked state, where a subset of oscillators remain close in phase while others drift away. Firstly, we derive an analytical criterion for the …
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Dynamical systems approach to one-dimensional spatiotemporal chaos -- A cyclist's view
… the extensive numerical exploration of the Kuramoto-Sivashinsky system in the chaotic regime: structure of the equilibrium solutions, our search for the shortest periodic orbits, description of the chaotic invariant set in terms of intrinsic coordinates and return maps on the Poincare …
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Synchronization for different opinions in Malaysia Multiracial Society: a mathematical exploration study
… of synchronization by 3 different models: Kuramoto model, Opinion Changing Rate model and a linear model associate with the famous Friedkin and Johnsen Model. We first develop a modified version of existing mathematical models and then conduct the numerical experiment on the models to …
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Exact coherent structures in spatiotemporal chaos: From qualitative description to quantitative predictions
… manifolds. Specifically, we investigate the Kuramoto-Sivashinsky equation, which describes the velocity of a flame front, and the Navier-Stokes equation for an incompressible fluid in a circular pipe. We argue with examples that this approach can lead to a theory of turbulence with predictive …
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Reduced-space Gaussian process regression forecast for nonlinear dynamical systems
… systems including the Lorenz 63, Lorenz 96, the Kuramoto-Sivashinsky, as well as a prototype climate model. We also study the performance of the proposed approach as the intrinsic dimensionality of the system attractor increases in highly turbulent regimes.
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Active flows and networks
… placed gap induces weak chimera states in Kuramoto-type oscillator networks, tunes or suppresses pattern formation in a generic Swift-Hohenberg model, and leads to persistent localization in a discrete Gross-Pitaevskii quantum network.
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Defying value-shift : how incumbents regain values in the industry with new technologies
Historically, incumbent assembly firms with unquestionable strong positions in such industries as the automobile, consumer electronics, computer and mobile phone industries, have lost power when new technology is introduced; at the same time, supplier firms have taken over the power and gained …
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Combinatorial aspects of synchronisation, percolation, and arithmetic
… combinatorics. In Chapter 2, we shall study the Kuramoto model, which is the prototypical model used for rigorous mathematical analysis in the field of synchronisation and nonlinear dynamics. A realisation of this model consists of a collection of identical oscillators with interactions given by …
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New methods for sensitivity analysis of chaotic dynamical systems
… and a chaotic Partial Differential Equation, the Kuramoto-Sivshinsky equation. The first method, the probability density adjoint method, forms a probability density function on the strange attractor associated with the system and uses its adjoint to find gradients. This was achieved using a novel …
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Coherence and synchronization of noisy-driven oscillators
… we develop a weakly nonlinear theory of the Kuramoto transition (a transition to collective synchrony) in an ensemble of globally coupled oscillators in presence of additional time-delayed coupling terms. We show that a linear delayed feedback not only controls the transition point, but …
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Theoretical modeling of pilot-wave hydrodynamics
… collective behavior is captured by a generalized Kuramoto model, which we explicitly derive from the boost framework. Finally, motivated by the statistical signature reported in the trajectories of droplets interacting with wells by Sáenz et al. (2020), we consider the stability of the steady …
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