Chemical oscillations

By Monika Sharma, Praveen Kumar. 2006

1,502 citations recorded by the source corpus.

Subfields: Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/b9524a2f7c21ea9e1187d07c4c18fc1c242800e3

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In Physical and Theoretical Chemistry

Citations in the corpus

Chimera states for coupled oscillators. (2004, background): “As they emphasize, nonlocal coupling [6, 7, 8] is less explored than local or global coupling [4, 5, 9, 10, 11, 12].”
Paths to synchronization on complex networks. (2006, background): “One of the most successful attempts to understand it is due to Kuramoto [8,9], who analyzed a model of phase oscillators coupled through the sine of their phase differences.”
Phase reduction approach to synchronisation of nonlinear oscillators (2016, methodology): “(46) describing coupled limit-cycle oscillators to coupled phase equations by treating the small heterogeneity of the oscillators and the mutual coupling as weak perturbations [2].”
Experimental observation of chimeras in coupled-map lattices (2012, methodology): “Considering the spatially continuous version of the 1D system in equation (1) (see Supplementary Information),”
Networks beyond pairwise interactions: structure and dynamics (2020, methodology): “Historically, this was made clear by Kuramoto and his mathematically tractable model of all-to-all coupled phase oscillators [355].”
Synchronization in complex networks (2008, background): “Next, without loss of generality, we can set φ = 0, which leads to the equations of motion (Kuramoto, 1975, 1984) θ̇i = ωi −Kr sin (θi) (i = 1, ..., N) .”
What are higher-order networks? (2021, background): “Moreover, the network interactions are often additive: For a network of Kuramoto oscillators [2, 163, 230]— one of the most prominent examples of network dynamical system—the joint effect of two oscillators on a third oscillator is just the sum of the two individual (nonlinear)”
Synchronization in complex oscillator networks and smart grids (2012, methodology): “2) PV buses with constant power loads: All load buses are PV buses, each load features a constant real power demand Pl,i > 0, and the load damping in [5] is neglected, that is, Di = 0 in equation [5].”
Synchronization processes in complex networks (2006, background): “One of the most successful attempts to understand synchronization phenomena was due to Kuramoto [20], who analyzed a model of phase oscillators coupled through the sine of their phase differences.”
Nonlinear fractional dynamics on a lattice with long range interactions (2005, background): “Another broad area of applications is related to the coupled system of oscillators with long-range interactions and the phenomenon of synchronization in the system [17]-[19].”
Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators (2009, methodology): “Another set of literature relevant to our investigation is the synchronization of coupled oscillators [6], in particular in the classic model introduced by Kuramoto [26].”
Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems (2016, background): “[8], a Kuramoto-type of phase dynamics [110,111] on the network is assumed, where a steady-state solution exists.”
The Dynamics of Modulated Wave Trains (2009, background): “Kuramoto [31] investigated more systematically the different types of phase equations that arise through formal multi-scale expansions depending on the symmetries of the underlying PDE and the stability and symmetry properties of the underlying periodic pattern (see also [43] for a comprehensive ove”
Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching (2019, methodology): “For a simplicial complex of N nodes we consider an extension of the network Kuramoto model [24] whose equations of motion are given by”
Distributed Probabilistic Synchronization Algorithms for Communication Networks (2008, background): “Synchronization phenomena have been a topic of research in the physical sciences and in mathematics for quite some time [1]–[26].”
Community detection in graphs (2009, methodology): “They used Kuramoto oscillators (Kuramoto, 1984), which are coupled two-dimensional vectors endowed with a proper frequency of oscillations.”
Macroscopic description for networks of spiking neurons (2015, background): “In the next section, we show that variables r and v can be related, via the same conformal map, to the Kuramoto order parameter, which is a macroscopic measure of phase coherence [43,44].”