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Mutually synchronized relaxation oscillators as prototypes of oscillating systems in biology

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What this work says

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

inferredcites →https://doi.org/10.1002/cpa.3160240607openalex-snapshot
Properties of solutions of ordinary differential equations with small parameters
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Ordinary Differential Equations
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Conditions for the application of the steady-state approximation to systems of differential equations
inferredcites →https://doi.org/10.1007/bf00364162openalex-snapshot
Synchronization of non-linear biochemical oscillators coupled by diffusion
inferredcites →https://doi.org/10.1007/bf02462209openalex-snapshot
Bifurcation analysis of reaction-diffusion equations—III. Chemical oscillations
inferredcites →https://doi.org/10.1007/bfb0013365openalex-snapshot
Self-entrainment of a population of coupled non-linear oscillators
inferredcites →https://doi.org/10.1016/0002-8703(64)90371-0openalex-snapshot
A computer model of atrial fibrillation
inferredcites →https://doi.org/10.1016/0010-4825(78)90003-3openalex-snapshot
Spectral analysis of coupled non-linear oscillators under modulation conditions with reference to intestinal modelling
inferredcites →https://doi.org/10.1016/0012-1606(73)90064-xopenalex-snapshot
Embryonic myocardial cell aggregates: Volume and pulsation rate
inferredcites →https://doi.org/10.1016/0014-4827(72)90199-1openalex-snapshot
Synchronization of pulsation rates in isolated cardiac myocytes
inferredcites →https://doi.org/10.1016/0016-0032(59)90191-7openalex-snapshot
Nonlinear problems in random theory
inferredcites →https://doi.org/10.1016/0022-5193(67)90051-3openalex-snapshot
Biological rhythms and the behavior of populations of coupled oscillators
inferredcites →https://doi.org/10.1016/0022-5193(71)90070-1openalex-snapshot
Populations of biochemical oscillators as circadian clocks
inferredcites →https://doi.org/10.1016/0022-5193(73)90164-1openalex-snapshot
Autowave processes in a distributed chemical system
inferredcites →https://doi.org/10.1016/0025-5564(67)90029-6openalex-snapshot
On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics
inferredcites →https://doi.org/10.1016/b978-0-12-547350-7.x5001-9openalex-snapshot
Biological Oscillators: their Mathematical Analysis
inferredcites →https://doi.org/10.1016/s0006-3495(61)86902-6openalex-snapshot
Impulses and Physiological States in Theoretical Models of Nerve Membrane
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A phase-shift model for the spatial and temporal organization of developing systems
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Differential Equations, Dynamical Systems, and Linear Algebra
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Nonlinear Problems in Random Theory
inferredcites →https://doi.org/10.1080/14786441108564652openalex-snapshot
LXXII.The heartbeat considered as a relaxation oscillation, and an electrical model of the heart
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LXXXVIII. On “relaxation-oscillations”
inferredcites →https://doi.org/10.1085/jgp.62.4.473openalex-snapshot
A Relaxation Oscillator Description of the Burst-Generating Mechanism in the Cardiac Ganglion of the Lobster, Homarus americanus
inferredcites →https://doi.org/10.1090/qam/30075openalex-snapshot
Relaxation oscillations
inferredcites →https://doi.org/10.1109/tcs.1974.1083848openalex-snapshot
Analytical solution of large numbers of mutually coupled nearly sinusoidal oscillators
inferredcites →https://doi.org/10.1109/tsmc.1973.4309322openalex-snapshot
Perturbation Methods in Applied Mathematics
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Thermodynamic Theory of Structure, Stability and Fluctuations
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Some Mathematics of Biological Oscillations
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A linked oscillator model of electrical activity of human small intestine
inferredcites →https://doi.org/10.2307/2004413openalex-snapshot
Perturbation Methods in Applied Mathematics
inferredcites →https://doi.org/10.2307/2316346openalex-snapshot
Ordinary Differential Equations.

What points at this work

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

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Redox rhythmicity: clocks at the core of temporal coherence
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Relaxation Oscillations
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Identical Oscillator Networks with Symmetry
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Relaxation Oscillations
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Direct Asymptotic Methods
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Relaxation Oscillations
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Computational and Mathematical Models of Neurons
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Temporal variability in a system of coupled mitotic timers
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The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model
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n:m Phase-locking of weakly coupled oscillators
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A reinvestigation of the Geman-Miller respiratory oscillator model
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The dynamics ofn weakly coupled identical oscillators
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Mode analysis of physiological oscillators intercoupled via pure time delays
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The mathematical modeling of entrained biological oscillators
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Asymptotic methods in mathematical biology
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A pacemaker cell pair model based on the phase response curve
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Mutual entrainment of two pacemaker cells. A study with an electronic parallel conductance model
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Computer models and automata theory in biology and medicine
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“Simpler Systems” and Invertebrate Systems
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NONLINEAR OSCILLATIONS (LIMIT CYCLES) IN PHYSICAL AND BIOLOGICAL SYSTEMS
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Exponential transient propagating oscillations in a ring of spiking neurons with unidirectional slow inhibitory synaptic coupling
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Effects of asymmetric coupling and self-coupling on metastable dynamical transient rotating waves in a ring of sigmoidal neurons
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Phase-locking dynamics for electronic relaxation oscillators via threshold pulse-modulation: Comparing experimental and analytical Arnold tongues
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Computational explorations into the dynamics of rings of coupled oscillators
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Relaxation oscillators with time delay coupling
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Asymptotic Methods for Relaxation Oscillations
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Pedagogical Approach to the Modeling and Simulation of Oscillating Chemical Systems with Modern Software: The Brusselator Model
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In-Phase, Anti-Phase and Fractured Synchrony in Ring Networks of Coupled Relaxation Electrochemical Oscillators
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Spectral Analysis of Stochastic Phase Lockings and Stochastic Bifurcations in the Sinusoidally Forced van der Pol Oscillator with Additive Noise
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On linearly coupled relaxation oscillations
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Phaselocking in a Reaction-Diffusion System with a Linear Frequency Gradient
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COLLECTIVE MODES OF THREE COUPLED RELAXATION OSCILLATORS: THE INFLUENCE OF DETUNING
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Computing with Biologically Inspired Neural Oscillators: Application to Colour Image Segmentation
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Synchronization of globally coupled oscillators without symmetry in the distribution of natural frequencies
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