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An equationfree approach to coupled oscillator dynamics: the Kuramoto model example
, 2005
"... We present an equationfree multiscale approach to the computational study of the collective dynamics of the Kuramoto model [Chemical Oscillations, Waves, and Turbulence, SpringerVerlag (1984)], a prototype model for coupled oscillator populations. Our study takes place in a reduced phase space of ..."
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Cited by 4 (1 self)
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We present an equationfree multiscale approach to the computational study of the collective dynamics of the Kuramoto model [Chemical Oscillations, Waves, and Turbulence, SpringerVerlag (1984)], a prototype model for coupled oscillator populations. Our study takes place in a reduced phase space
From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators
 Phys. D
, 2000
"... The Kuramoto model describes a large population of coupled limitcycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certain threshold, the system exhibits a phase transition: some of the oscillators spontaneously synchronize, w ..."
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Cited by 300 (4 self)
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The Kuramoto model describes a large population of coupled limitcycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certain threshold, the system exhibits a phase transition: some of the oscillators spontaneously synchronize
On the Critical Coupling for Kuramoto Oscillators
 SIAM Journal on Applied Dynamical Systems
"... Abstract. The celebrated Kuramoto model captures various synchronization phenomena in biological and manmade dynamical systems of coupled oscillators. It is wellknown that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency to synchronizatio ..."
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Cited by 16 (9 self)
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Abstract. The celebrated Kuramoto model captures various synchronization phenomena in biological and manmade dynamical systems of coupled oscillators. It is wellknown that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency
A Structural Approach to Operational Semantics
, 1981
"... Syntax of a very simple programming language called L. What is abstract about it will be discussed a little here and later at greater length. For us syntax is a collection of syntactic sets of phrases; each set corresponds to a different type of phrase. Some of these sets are very simple and can be ..."
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Cited by 1541 (3 self)
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Syntax of a very simple programming language called L. What is abstract about it will be discussed a little here and later at greater length. For us syntax is a collection of syntactic sets of phrases; each set corresponds to a different type of phrase. Some of these sets are very simple and can be taken as given: Truthvalues This is the set T = ftt; ffg and is ranged over by (the metavariable) t (and we also happily employ for this (and any other) metavariable sub and superscripts to generate other metavariables: t ; t 0 ; t 1k ).
ON THE CRITICAL COUPLING FOR KURAMOTO OSCILLATORS ∗
"... Abstract. The celebrated Kuramoto model captures various synchronization phenomena in biological and manmade dynamical systems of coupled oscillators. It is wellknown that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency to synchronizatio ..."
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Abstract. The celebrated Kuramoto model captures various synchronization phenomena in biological and manmade dynamical systems of coupled oscillators. It is wellknown that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency
Fast Parallel Algorithms for ShortRange Molecular Dynamics
 JOURNAL OF COMPUTATIONAL PHYSICS
, 1995
"... Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of interatomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dyn ..."
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Cited by 622 (6 self)
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dynamics models which can be difficult to parallelize efficiently  those with shortrange forces where the neighbors of each atom change rapidly. They can be implemented on any distributedmemory parallel machine which allows for messagepassing of data between independently executing processors
Impulses and Physiological States in Theoretical Models of Nerve Membrane
 Biophysical Journal
, 1961
"... ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing excitabi ..."
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Cited by 496 (0 self)
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ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing
Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of nalkanes
 J. Comput. Phys
, 1977
"... A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method ..."
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Cited by 682 (6 self)
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model, (b) the derivation of the equations of motion of the system and (c) the choice of an efficient algorithm for the numerical integration of these equations. In polyatomic molecules, the fast internal vibrations are usually decoupled from
Excitatory and inhibitory interactions in localized populations of model
 Biophysics
, 1972
"... ABSMAcr Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The res ..."
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Cited by 491 (11 self)
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ABSMAcr Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli
Results 1  10
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382,458