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Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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Cardiac Arrhythmias: Their Mechanisms, Diagnosis, and Management
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Frequency Entrainment of a Forced van der Pol Oscillator
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Period Three Implies Chaos
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A Second Order Differential Equation with Singular Solutions
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Physiology of Membrane Disorders
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The Geometry of Biological Time
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A simple model for phase locking of biological oscillators
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On cardiac arrythmias: AV conduction block
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The response of excitable membrane models to a cyclic input
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On visual detection of light sources
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Trajectory divergence for coupled relaxation oscillators: Measurements and models
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On the bifurcation of maps of the interval
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A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line
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Frequency entrainment of squid axon membrane
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A mathematical model for first degree block and the Wenckebach phenomenon
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Mesure de Lebesgue et Nombre de Rotation
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The cardiac pacemaker: Effects of regularly spaced nervous input
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Mathematical relationship between automaticity of the sinus node and the AV junction
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Principles of Cardiac Arrhythmias
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The disorders of cardiac rhythm
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A biologic model of parasystole
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The mechanism of A-V arrhythmias
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A mathematical model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators
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Mutual entrainment of two pacemaker cells. A study with an electronic parallel conductance model
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Unstable dynamics of a periodically driven oscillator in the presence of noise
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On finite limit sets for transformations on the unit interval
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Symbolic dynamics and relaxation oscillations
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The simplest case of a strange attractor
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Fluctuations and the onset of chaos
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Biological Oscillators: their Mathematical Analysis
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Interaction of oscillators: Effect of sinusoidal stretching of the sinoatrial node on nodal rhythm
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Mechanism of atrioventricular conduction: Study on an analogue
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Simple mathematical models with very complicated dynamics
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Period Three Implies Chaos
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LXXII.The heartbeat considered as a relaxation oscillation, and an electrical model of the heart
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Dynamics of Encoding in a Population of Neurons
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Qualitative analysis of the periodically forced relaxation oscillations
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Chaotic Behavior in Piecewise Continuous Difference Equations
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Electrophysiological and mathematical characteristics of the escape rhythm during complete AV block
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Chaotic States of Anharmonic Systems in Periodic Fields
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ORDINARY DIFFERENTIAL EQUATIONS
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On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1- y 2 )y˙ + y = b λ k cos(λ l + α), k Large
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A quantitative description of membrane current and its application to conduction and excitation in nerve
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Reconstruction of the electrical activity of cardiac Purkinje fibres.
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Pacemaker Neurons: Effects of Regularly Spaced Synaptic Input
inferredcites →https://doi.org/10.1126/science.7313693openalex-snapshot
Phase Locking, Period-Doubling Bifurcations, and Irregular Dynamics in Periodically Stimulated Cardiac Cells
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Phase Control of Neural Pacemakers
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ELECTRICAL AXIS DEVIATION OF FIFTY NORMAL ELECTROCARDIOGRAMS
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Integrate-and-Fire Models of Nerve Membrane Response to Oscillatory Input
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THE BEHAVIOR OF ATRIO–VENTRICULAR NODAL RHYTHM FOLLOWING DIRECT PERFUSION OF THE SINUS NODE
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Chaotic Behaviour of Deterministic Orbits: The Problem of Turbulent Phase
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Stimulus-response relationship in dog ventricle in vivo
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Synchronization of the heart.
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Aplysia bursting neurons as endogenous oscillators. II. Synchronization and entrainment by pulsed inhibitory synaptic input
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A mathematical model of parasystole and its application to clinical arrhythmias.
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Correlative electrophysiological and anatomical studies concerning the site of origin of escape rhythm during complete atrioventricular block in the dog.
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A Second Order Differential Equation with Singular Solutions
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Disorders of Cardiac Rhythm
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Cardiac Arrhythmias: Their Mechanisms, Diagnosis, and Management.
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Clinical Disorders of the Heart Beat.
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Clinical Disorders of the Heart Beat.
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Physiology of Membrane Disorders.
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Principles of Cardiac Arrhythmias.
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Nonlinear Analysis of Physiological Control Systems
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Anatomy of the sinus node, av node, and his bundle of the heart of the sperm whale (Physeter macrocephalus), with a note on the absence of an os cordis
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Topological patterns of synchronization in the biological oscillator
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The Cardiac Conducting System and Its Autonomic Control
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Models of the Atrioventricular Node
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Resonant Pattern Formation in a Spatially Extended Chemical System
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Low-Dimensional Dynamics in the Heart
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Nonlinear Dynamics at the Bedside
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Spectral Kinetics: Study of Complex Reactions by External Perturbations
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Phase Resetting Neural Oscillators: Topological Theory Versus the RealWorld
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Chaos in Physiology: Health or Disease?
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Patterns of Activity in a Reduced Ionic Model of a Cell from the Rabbit Sinoatrial Node
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Periodic Forcing of a Biochemical System with Multiple Modes of Oscillatory Behaviour
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Human Brain Oscillations: From Physiological Mechanisms to Analysis and Cognition
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Will We Continue to Use Chaotic Attractors in Science for a Long Time, or Will They only Be a Passing Curiosity?
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Sudden Cardiac Death and Turbulence
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Human Brain Oscillations: From Physiological Mechanisms to Analysis and Cognition
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Modeling Fireflies Synchronization
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The Telegraph Plant: Codariocalyx motorius (Formerly Also Desmodium gyrans)
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Human Brain Oscillations: From Physiological Mechanisms to Analysis and Cognition
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Dimension, Fractal Measures, and Chaotic Dynamics
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Afterpotentials and Pacemaker Oscillations in an Ionic Model of Cardiac Purkinje Fibres
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Spectral Kinetics and the Efficiency of (Bio) Chemical Reactions
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Order in Time: How the Cooperation Between the Hands Informs the Design of the Brain
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Experimental Studies of Chaotic Neural Behavior: Cellular Activity and Electroencephalographic Signals
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Continuation of Arnold Tongues in Mathematical Models of Periodically Forced Biological Oscillators
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Computational and Mathematical Models of Neurons
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Free vibration of two coupled nonlinear oscillators
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Symmetry-breaking bifurcation: A possible mechanism for 2:1 frequency-locking in animal locomotion
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Frequency-induced phase transitions in bimanual tapping
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Regular and chaotic behaviour of cardiac cells stimulated at frequencies between 2 and 20 Hz
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Entrainment in pacemakers characterized by a V-shaped PRC
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Phase locking of biological clocks
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The heart as a system of coupled nonlinear oscillators
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Periodic pulsatile stimulation of a nonlinear oscillator
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Global bifurcations of a periodically forced nonlinear oscillator
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1?1 and 2?1 phase entrainment in a system of two coupled limit cycle oscillators
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Fibrillation of a cardiac region and the tachycardia mode of a two-oscillator system
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Suppression of pacemaker activity by rapid repetitive phase delay
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On the relationship between two models of neural entrainment
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Is the normal heart a periodic oscillator?
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A comparison between transitions induced by random and periodic fluctuations
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Discrete models for chemically reacting systems
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Map dependence of the fractal dimension deduced from iterations of circle maps
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Parameter-dependent transitions and the optimal control of dynamical diseases
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Chaotic motion of an impact oscillator
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Phase resetting control based on direct phase response curve
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Analysis of unstable behavior in a mathematical model for erythropoiesis
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Response of an oscillatory differential delay equation to a single stimulus
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Response of an oscillatory differential delay equation to a periodic stimulus
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Mechanisms for synchrony and alternation in song interactions of the bushcricket Mecopoda elongata (Tettigoniidae: Orthoptera)
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Phase resetting for a network of oscillators via phase response curve approach
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On Hebbian-like adaptation in heart muscle: a proposal for 'cardiac memory'
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The variance of phase-resetting curves
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A quantitative model of relation between respiratory-related blood pressure fluctuations and the respiratory sinus arrhythmia
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Functional Characterization of Oscillatory and Excitable Media
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Annihilation, entrainment and modulation of ventricular parasystolic rhythms
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Entrainment of atrioventricular nodal reentrant tachycardias during overdrive pacing from high right atrium and coronary sinus
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Experiments on bifurcations to chaos in a forced chemical reactor
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Difference equation model of ventricular parasystole as an interaction between cardiac pacemakers based on the phase response curve
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Coupled oscillators and the design of central pattern generators
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Age-structured and two-delay models for erythropoiesis
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Ionic mechanisms and nonlinear dynamics of embryonic chick heart cell aggregates
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Parallel implementation of a general purpose functional predictor for chaotic time series
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On the arithmetic of phase locking: Coupled neurons as a lattice on R2
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Bifurcation and chaos in a periodically stimulated cardiac oscillator
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Chaos in the Beeler-Reuter system for the action potential of ventricular myocardial fibres
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Nonlinear dynamics of the heartbeat
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Universality and self-similarity in the bifurcations of circle maps
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Some observations on the question: Is ventricular fibrillation “chaos”?
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Dynamic regimes in a periodically forced reaction cell with oscillatory chemical reaction
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Coupled relaxation oscillators and circle maps
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Symbolic dynamics and skeletons of circle maps
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Global bifurcation structure in periodically stimulated giant axons of squid
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Ventricular fibrillation-defibrillation in the toad Bufo paracnemis
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Pathology of the pacemaker network
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Why are so many biological systems periodic?
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Bistability, period doubling bifurcations and chaos in a periodically forced oscillator
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Self-similarity in periodically forced oscillators
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Experimental observations of periodic and chaotic regimes in a forced chemical oscillator
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Complex dynamics resulting from repeated stimulation of nonlinear oscillators at a fixed phase
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Resonance behaviour in two-parameter families of periodically forced oscillators
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Isochrones and the dynamics of kicked oscillators
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Alternans in periodically stimulated isolated ventricular myocytes: Experiment and model
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Is the isolated heart a relaxation-oscillator?
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Tuning the brain rhythms: How internal coherence influences network entrainment by tACS
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Chaotic discretization theorems for forced linear and nonlinear coupled oscillators
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A matrix-based approach to solving the inverse Frobenius–Perron problem using sequences of density functions of stochastically perturbed dynamical systems
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Back pain and the homoeostatic requirements of the spinal system
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Computational analysis of financial system through non-integer derivative
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Propensity of a circadian clock to adjust to the 24h day–night light cycle and its sensitivity to molecular noise
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Continuation and bifurcation analysis of a periodically forced excitable system
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Existence and Stability Criteria for Global Synchrony and for Synchrony in two Alternating Clusters of Pulse-Coupled Oscillators Updated to Include Conduction Delays
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Chaos in the genesis and maintenance of cardiac arrhythmias
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Analytic approximations of statistical quantities and response of noisy oscillators
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A minimal model for synaptic integration in simple neurons
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Unraveling multiple 1:1 entrainment regions in the Arnold onion diagram: A study of the circadian Novak–Tyson model
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Dynamic entrainment of neuronal spiking: A phase plane analysis and a data-driven approach
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Characterization of the dynamics of free and excited Grudzinski-Zebrowski (GZ) oscillator using mathematical methods and microcontroller simulation experiment
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The influences of the ionic channel conductances and kinetics on the phase-locking behaviors of modeled sinoatrial node cells and tissue
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Nonlinear and stochastic dynamics in the heart
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Phase resetting of the rhythmic activity of embryonic heart cell aggregates. Experiment and theory
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Evidence for chaotic behavior in driven ventricles
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Theoretical computation of phase locking in embryonic atrial heart cell aggregates
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Chaotic dynamics in an ionic model of the propagated cardiac action potential
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A qualitative model of a motor circadian rhythm
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Chaotic behavior in a dissipative non-ideal periodically kicked rotator
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Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems
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Entrainment of circus movement tachycardia utilizing an accessory pathway with long retrograde conduction times during ventricular and atrial stimulation
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Catheter ablation of atrioatrial conduction as a cure for atrial arrhythmia after orthotopic heart transplantation11Preliminary results have been published in an abstract format at the 1996 American College of Cardiology meeting in Orlando.
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An Asymmetrical Phase Locking Structure for aNon-excitable Cell Model
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Bifurcation Structure of a Periodically Driven Nerve Pulse Equation Modelling Cardiac Conduction
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Lock-in phenomenon of vortex shedding in oscillatory flows: an analytical investigation pertaining to combustors
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Optimal waveform for fast synchronization of airfoil wakes
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Chaos in biological systems
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Complex Patterns in a Periodically Forced Surface Reaction
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Entrainment, Instability, Quasi-periodicity, and Chaos in a Compound Neural Oscillator
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Resonance constraints on rhythmic movement.
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Nonlinear dynamics: Simplicity and universality in the transition to chaos
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Period multupling-evidence for nonlinear behaviour of the canine heart
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Synchronization and rhythmic processes in physiology
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Phase-selective entrainment of nonlinear oscillator ensembles
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Higher-order and fractional discrete time crystals in clean long-range interacting systems
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A simple method for detecting chaos in nature
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Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory
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Dynamics of Parkinsonian tremor during deep brain stimulation
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Cardiac arrhythmias and circle maps−A classical problem
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Bifurcation structures of periodically forced oscillators
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Periodically kicked hard oscillators
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Discrete-time stimulation of the oscillatory and excitable forms of a FitzHugh–Nagumo model applied to the pulsatile release of luteinizing hormone releasing hormone
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Alternans and higher-order rhythms in an ionic model of a sheet of ischemic ventricular muscle
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Generation of multiple attractors and nonequilibrium phase transitions
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Effects of periodic perturbations on the oscillatory combustion of acetaldehyde
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Effects of two periodic perturbations on the oscillatory combustion of acetaldehyde
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Observations of a torus in a model of the Belousov–Zhabotinskii reaction
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Inhomogeneous perturbations and phase resetting in an oscillatory reaction–diffusion system
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High frequency stimulation of cardiac myocytes: A theoretical and computational study
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Complex mixed-mode oscillatory patterns in a periodically forced excitable Belousov-Zhabotinsky reaction model
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A bifurcation giving birth to order in an impulsively driven complex system
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Chaos and geometrical resonance in the damped pendulum subjected to periodic pulses
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Role of intracellular calcium cycling in sinoatrial node myocyte phase-locking
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Success rate analysis of the response of an excitable laser to periodic perturbations
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The emergence of polyglot entrainment responses to periodic inputs in vicinities of Hopf bifurcations in slow-fast systems
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Dynamic entrainment: A deep learning and data-driven process approach for synchronization in the Hodgkin–Huxley model
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Polyglot entrainment for higher dimensional neuronal models
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The Challenge of Complex Dynamics for Theoretical Models of Cardiac Activity
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Structure of the parameter space for the van der Pol oscillator
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Nonlinear dynamics, chaos and complex cardiac arrhythmias
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Deep learning-based classification of complex intracellular calcium concentration patterns
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Subharmonic bifurcation in the sine map: An infinite hierarchy of cusp bistabilities
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Global bifurcations of a periodically forced biological oscillator
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Disappearance of chaos and integrability in an externally modulated nonlinear oscillator
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Scaling relations at the critical line and the period-doubling route for the sine map and the driven damped pendulum
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Phase locking, period doubling, and chaotic phenomena in externally driven excitable systems
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Entrainment effects in an acoustooptic bistable device with delayed feedback
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Periodic forcing of a limit-cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations
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Entrainment and termination of reentrant wave propagation in a periodically stimulated ring of excitable media
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Predicting the entrainment of reentrant cardiac waves using phase resetting curves
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Well-behaved dynamics in a dissipative nonideal periodically kicked rotator
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Phase resetting, phase locking, and bistability in the periodically driven saline oscillator: Experiment and model
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Bifurcation analysis of a periodically forced relaxation oscillator: Differential model versus phase-resetting map
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Phase-locking behaviors in an ionic model of sinoatrial node cell and tissue
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Global dynamics of a stochastic neuronal oscillator
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High-frequency forced oscillations in neuronlike elements
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Quantifying the degree of locking in weakly forced stochastic systems
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Robust Convergence in Pulse-Coupled Oscillators with Delays
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Fine Structure of Phase Locking
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Symmetric kicked self-oscillators: Iterated maps, strange attractors, and symmetry of the phase-locking Farey hierarchy
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Direct memory access methods applied to chaotic behavior experiments
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Nonlinear Analysis of Physiological Control Systems
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Minimum energy subharmonic synchronization of an uncertain nonlinear oscillator
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Cardiac dysrhythmias-a phenomenon of chaos
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Open-Loop Control Design for Contraction in Affine Nonlinear Systems
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Coupled seismic faults and the predictability of earthquakes by means of deterministic models
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Right Atrial‐ventricular Dissociation and Entrainment while Pacing from High Right Atrium and Coronary Sinus during Circus Movement Tachycardias
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Ventricular Tachycardia with Alternating Cycle Lengths: Self‐Entrainment of Parasystolic Rhythm?
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Resetting and Transient Entrainment of Ventricular Tachycardia
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Transient Entrainment: The Evolution of a Medical Concept from Description to Prescription
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Existence of Bistability and Correlation with Arrhythmogenesis in Paced Sheep Atria
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Universal Bifurcations and the Classification of Cardiac Arrhythmiasa
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Applications of Nonlinear Dynamics to Clinical Cardiologya
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Rhythms Produced by High‐Amplitude Periodic Stimulation of Spontaneously Beating Aggregates of Embryonic Chick Ventricular Myocytesa
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Mechanisms Underlying Ventricular Tachycardia and Fibrillation in the Ischemic Heart: Relation to Nonlinear Dynamicsa
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Complex Bifurcations and Chaos in Simple Theoretical Models of Cardiac Oscillationsa
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The emergence of subcellular pacemaker sites for calcium waves and oscillations
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Theoretical and Experimental Study of an Electromechanical System Actuated by a Brusselator Electronic Circuit Simulator
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Phase Locking, Period-Doubling Bifurcations, and Irregular Dynamics in Periodically Stimulated Cardiac Cells
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