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The mathematical modeling of entrained biological 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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The Circadian System of Man
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The Circadian System of Man
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Differential Equations with Small Parameters and Relaxation Oscillations
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The Belousov-Zhabotinskii Reaction
inferredcites →https://doi.org/10.1007/978-3-662-22492-2openalex-snapshot
The Geometry of Biological Time
inferredcites →https://doi.org/10.1007/bf00275153openalex-snapshot
A simple model for phase locking of biological oscillators
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The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model
inferredcites →https://doi.org/10.1007/bf00276130openalex-snapshot
On cardiac arrythmias: AV conduction block
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n:m Phase-locking of weakly coupled oscillators
inferredcites →https://doi.org/10.1007/bf00276928openalex-snapshot
Mutually synchronized relaxation oscillators as prototypes of oscillating systems in biology
inferredcites →https://doi.org/10.1007/bf00326666openalex-snapshot
The response of excitable membrane models to a cyclic input
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Suppression of pacemaker activity by rapid repetitive phase delay
inferredcites →https://doi.org/10.1007/bf00364162openalex-snapshot
Synchronization of non-linear biochemical oscillators coupled by diffusion
inferredcites →https://doi.org/10.1007/bf00387210openalex-snapshot
Pulse sequences generated by a degenerate analog neuron model
inferredcites →https://doi.org/10.1007/bf02231729openalex-snapshot
Simulation of the electric-control activity of the stomach by an array of relaxation oscillators
inferredcites →https://doi.org/10.1007/bf02462209openalex-snapshot
Bifurcation analysis of reaction-diffusion equations—III. Chemical oscillations
inferredcites →https://doi.org/10.1007/bfb0013294openalex-snapshot
International Symposium on Mathematical Problems in Theoretical Physics
inferredcites →https://doi.org/10.1007/bfb0013365openalex-snapshot
Self-entrainment of a population of coupled non-linear oscillators
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(80)90308-2openalex-snapshot
Mutual entrainment of two pacemaker cells. A study with an electronic parallel conductance model
inferredcites →https://doi.org/10.1016/0025-5564(70)90122-7openalex-snapshot
Ensemble entrainment of self-sustaining oscillators: a possible application to neural signals
inferredcites →https://doi.org/10.1016/0167-2789(80)90014-7openalex-snapshot
Symbolic dynamics and relaxation oscillations
inferredcites →https://doi.org/10.1016/0167-2789(83)90014-3openalex-snapshot
On the arithmetic of phase locking: Coupled neurons as a lattice on R2
inferredcites →https://doi.org/10.1016/s0079-6123(08)60974-7openalex-snapshot
Progress in Brain Research
inferredcites →https://doi.org/10.1016/s0079-6123(08)60995-4openalex-snapshot
Models of Neuronal Populations: The Basic Mechanisms of Rhythmicity
inferredcites →https://doi.org/10.1038/scientificamerican0583-144openalex-snapshot
Sudden Cardiac Death: A Problem in Topology
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Nonlinear Problems in Random Theory
inferredcites →https://doi.org/10.1080/14786435908243273openalex-snapshot
The propagation of fading waves
inferredcites →https://doi.org/10.1080/14786441108564652openalex-snapshot
LXXII.The heartbeat considered as a relaxation oscillation, and an electrical model of the heart
inferredcites →https://doi.org/10.1085/jgp.83.4.613openalex-snapshot
Phase resetting properties of cardiac pacemaker cells.
inferredcites →https://doi.org/10.1103/physrevlett.48.1772openalex-snapshot
Fine Structure of Phase Locking
inferredcites →https://doi.org/10.1126/science.200.4337.48openalex-snapshot
Periodicity and Chaos in Coupled Nonlinear Oscillators
inferredcites →https://doi.org/10.1126/science.7313693openalex-snapshot
Phase Locking, Period-Doubling Bifurcations, and Irregular Dynamics in Periodically Stimulated Cardiac Cells
inferredcites →https://doi.org/10.1137/0138026openalex-snapshot
Large Populations of Coupled Chemical Oscillators
inferredcites →https://doi.org/10.1137/0515019openalex-snapshot
Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.
inferredcites →https://doi.org/10.1139/y83-092openalex-snapshot
Phase locking of the respiratory rhythm in cats to a mechanical ventilator
inferredcites →https://doi.org/10.2307/1421454openalex-snapshot
Biological Rhythms in Human and Animal Physiology
inferredcites →https://doi.org/10.5694/j.1326-5377.1972.tb88192.xopenalex-snapshot
Biological Rhythms in Human and Animal Physiology
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1002/bbpc.19850890617openalex-snapshot
Observation of Entrainment, Quasiperiodicity and Chaos in Glycolyzing Yeast Extracts under Periodic Glucose Input
inferred← citeshttps://doi.org/10.1007/978-3-319-12316-5_5openalex-snapshot
Direct Asymptotic Methods
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Dynamic Coupling and Time Patterns in Biochemical Processes
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A spike generator mechanism model simulates utricular afferents response to sinusoidal vibrations
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Periodic and chaotic behavior of substrate-inhibited enzymatic reactions with hydrogen ions production
inferred← citeshttps://doi.org/10.1007/s10439-005-9010-7openalex-snapshot
Neuronal Electrical Rhythms Described by Composite Mapped Clock Oscillators
inferred← citeshttps://doi.org/10.1016/0042-6989(89)90147-8openalex-snapshot
Frequency transfer properties of the spike generating mechanism of cat retinal ganglion cells
inferred← citeshttps://doi.org/10.1016/0167-2789(85)90004-1openalex-snapshot
Nonlinear dynamics of the heartbeat
inferred← citeshttps://doi.org/10.1016/0270-0255(86)90089-8openalex-snapshot
Computer models and automata theory in biology and medicine
inferred← citeshttps://doi.org/10.1016/0960-0779(94)00205-5openalex-snapshot
Chaotic behaviour of an acetylcholinesterase enzyme system
inferred← citeshttps://doi.org/10.1016/j.bpj.2009.04.016openalex-snapshot
Phase Resetting Curves Allow for Simple and Accurate Prediction of Robust N:1 Phase Locking for Strongly Coupled Neural Oscillators
inferred← citeshttps://doi.org/10.1016/j.jde.2009.07.034openalex-snapshot
Persistence of periodic patterns for perturbed biological oscillators
inferred← citeshttps://doi.org/10.1023/a:1024422802673openalex-snapshot
Dendritic Synchrony and Transient Dynamics in a Coupled Oscillator Model of the Dopaminergic Neuron
inferred← citeshttps://doi.org/10.1023/b:abme.0000030238.50895.f0openalex-snapshot
Stochastic and Coherence Resonance in an In Silico Neural Model
inferred← citeshttps://doi.org/10.1111/j.1749-6632.1987.tb48725.xopenalex-snapshot
Frequency Modulation Dynamics in Neural Networksa
inferred← citeshttps://doi.org/10.1137/s0036139900368807openalex-snapshot
Synchronization and Transient Dynamics in the Chains of Electrically Coupled Fitzhugh--Nagumo Oscillators
inferred← citeshttps://doi.org/10.3182/20020721-6-es-1901.01099openalex-snapshot
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