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The behavior of rings of coupled oscillators

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Plane Wave Solutions to Reaction‐Diffusion Equations
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Asymptotic Behavior of Stationary Homogeneous Neuronal Nets
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The Geometry of Biological Time
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Temporal oscillations in neuronal nets
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Waves in a simple, excitable or oscillatory, reaction-diffusion model
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n:m Phase-locking of weakly coupled oscillators
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Mutually synchronized relaxation oscillators as prototypes of oscillating systems in biology
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A mathematical theory of visual hallucination patterns
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Synchronization of non-linear biochemical oscillators coupled by diffusion
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Simulation of the electric-control activity of the stomach by an array of relaxation oscillators
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The stability of entrainment conditions forRLC coupled van der pol oscillators used as a model for intestinal electrical rhythms
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Bifurcation of periodic motions in two weakly coupled van der Pol oscillators
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Two coupled neural oscillators as a model of the circadian pacemaker
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Diffusion-induced morphogenesis in the development of Dictyostelium
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Simulation of intrinsic bursting in CA3 hippocampal neurons
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The stability of entrainment conditions for coupled van der pol oscillators used as a model for intestinal electrical rhythms
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Dynamical Model of the Human Small Intestine
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On the stability of steady finite amplitude convection
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Bifurcation involving the hexagonal lattice
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Mathematical Modeling of the Colorectal Myoelectrical Activity in Humans
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Frequency Entrainment of Coupled Hodgkin-Huxley-Type Oscillators for Modeling Gastro-Intestinal Electrical Activity
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Cellular Mechanism of Neuronal Synchronization in Epilepsy
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Slowly Modulated Oscillations in Nonlinear Diffusion Processes
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Coupled Chemical Oscillators
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Spiral Waves in Reaction-Diffusion Equations
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Patterns at Primary Hopf Bifurcations of a Plexus of Identical Oscillators
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On the Validity of the Two-Timing Method for Large Times
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Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.
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Simulation of the electrical and mechanical gradient of the small intestine

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Conditions and Linear Stability Analysis at the Transition to Synchronization of Three Coupled Phase Oscillators in a Ring
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COLLECTIVE MODES OF THREE COUPLED RELAXATION OSCILLATORS: THE INFLUENCE OF DETUNING
inferred← citeshttps://doi.org/10.1162/089976600300015907openalex-snapshot
Dynamics of Strongly Coupled Spiking Neurons
inferred← citeshttps://doi.org/10.1162/089976602753633376openalex-snapshot
The Influence of Limit Cycle Topology on the Phase Resetting Curve
inferred← citeshttps://doi.org/10.1162/neco_a_00536openalex-snapshot
Local Linear Approximation of the Jacobian Matrix Better Captures Phase Resetting of Neural Limit Cycle Oscillators
inferred← citeshttps://doi.org/10.1186/s13408-015-0033-6openalex-snapshot
Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience
inferred← citeshttps://doi.org/10.1209/0295-5075/97/40005openalex-snapshot
Synchronizing large number of nonidentical oscillators with small coupling
inferred← citeshttps://doi.org/10.1209/epl/i1997-00159-8openalex-snapshot
Size instabilities in rings of chaotic synchronized systems
inferred← citeshttps://doi.org/10.1364/josaa.19.001049openalex-snapshot
Neural grouping and geometric effect in the determination of apparent orientation
inferred← citeshttps://doi.org/10.3182/20071017-3-br-2923.00013openalex-snapshot
SINGLE INTERCONNECTION OF KURAMOTO COUPLED OSCILLATORS
inferred← citeshttps://doi.org/10.3389/fncom.2012.00067openalex-snapshot
A computational role for bistability and traveling waves in motor cortex
inferred← citeshttps://doi.org/10.3390/photonics10070813openalex-snapshot
Route to Chaos in a Unidirectional Ring of Three Diffusively Coupled Erbium-Doped Fiber Lasers
inferred← citeshttps://doi.org/10.3390/qubs8040027openalex-snapshot
Optical Energy Increasing in a Synchronized Motif-Ring Array of Autonomous Erbium-Doped Fiber Lasers
inferred← citeshttps://doi.org/10.5206/mase/14147openalex-snapshot
Cluster solutions in networks of weakly coupled oscillators on a 2D square torus
inferred← citeshttps://doi.org/10.5772/6026openalex-snapshot
Almost Global Synchronization of Symmetric Kuramoto Coupled Oscillators
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