Stably Rotating Patterns of Reaction and Diffusion

Deterministic Nonperiodic Flow

1963 • 18,282 citations

The chemical basis of morphogenesis

1952 • 11,233 citations

Simple mathematical models with very complicated dynamics

1976 • 6,489 citations

Self-Organization in Nonequilibrium Systems

1977 • 5,342 citations

An equation for continuous chaos

1976 • 3,714 citations

Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System

1970 • 1,839 citations

Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system

1972 • 1,438 citations

Bifurcations and Dynamic Complexity in Simple Ecological Models

1976 • 1,239 citations

Spiral Waves of Chemical Activity

1972 • 1,200 citations

Circus movement in rabbit atrial muscle as a mechanism of tachycardia. III. The "leading circle" concept: a new model of circus movement in cardiac tissue without the involvement of an anatomical obstacle.

1977 • 1,069 citations

Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium

1976 • 984 citations

Circus movement in rabbit atrial muscle as a mechanism of trachycardia.

1973 • 689 citations

Dissipative structure: An explanation and an ecological example

1972 • 671 citations

Nagumo's equation

1970 • 492 citations

Oscillatory Phenomena in Biochemistry

1971 • 486 citations

Circus Movement in Rabbit Atrial Muscle as a Mechanism of Tachycardia

1973 • 453 citations

Changes of Action Potential Shape and Velocity for Changing Core Conductor Geometry

1974 • 440 citations

Traveling Wave Solutions of a Nerve Conduction Equation

1973 • 412 citations

Plane Wave Solutions to Reaction‐Diffusion Equations

1973 • 402 citations

The dynamics of density dependent population models

1977 • 398 citations

The Theory of Oscillating Reactions - Kinetics Symposium

1967 • 308 citations

Biological and Biochemical Oscillators

1973 • 293 citations

Autowave processes in a distributed chemical system

1973 • 292 citations

Rotating Chemical Reactions

1974 • 287 citations

Chaotic Behavior in Simple Reaction Systems

1976 • 272 citations

Thresholds in development

1977 • 247 citations

Conduction of the Cardiac Impulse

1971 • 244 citations

Chapter 6 Cell Aggregation and Differentiation in Dictyostelium

1968 • 242 citations

Experimental evidence of chaotic states in the Belousov–Zhabotinskii reaction

1977 • 241 citations

Chemical oscillations

1973 • 216 citations

Simulation of slow-wave electrical activity of small intestine

1971 • 187 citations

Combinatorial and topological methods in nonlinear chemical kinetics

1975 • 185 citations

Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction

1974 • 185 citations

Conduction of the Cardiac Impulse

1972 • 180 citations

OSCILLATORY ENZYMES

1976 • 164 citations

Patterns of phase compromise in biological cycles

1974 • 159 citations

Control Circuits for Determination and Transdetermination

1973 • 153 citations

A Thermally Excited Non-Linear Oscillator

1966 • 151 citations

Theory of propagation of discontinuities in kinetic systems with multiple time scales: Fronts, front multiplicity, and pulses

1975 • 150 citations

Intracellular Transport

1966 • 149 citations

AN EXPANDING ROLE FOR GAS CHROMATOGRAPHY: MEASUREMENT OF PHYSICAL AND CHEMICAL PARAMETERS

1967 • 142 citations

Simulation of the electric-control activity of the stomach by an array of relaxation oscillators

1972 • 140 citations

Pattern formation in reacting and diffusing systems

1976 • 138 citations

Analysis and control of immobilized enzyme systems

1977 • 132 citations

On a variety of wave phenomena in chemical reactions

1974 • 132 citations

Chemical reaction dynamics

1974 • 130 citations

Bistability caused by Substrate Inhibition of Peroxidase in an Open Reaction System

1968 • 129 citations

Different Types of Chaos in Two Simple Differential Equations

1976 • 129 citations

Simulation of the electrical and mechanical gradient of the small intestine

1968 • 126 citations

Conduction of the Cardiac Impulse

1971 • 122 citations

Metabolic coupling and synchronization of NADH oscillations in yeast cell populations

1971 • 117 citations

Control of mitosis by a continuous biochemical oscillation: Synchronization; spatially inhomogeneous oscillations

1975 • 116 citations

Interactions of Reaction and Diffusion in Open Systems

1969 • 113 citations

A study of pace‐maker activity in intestinal smooth muscle

1974 • 113 citations

Phase waves in oscillatory chemical reactions

1973 • 112 citations

Bifurcation analysis of nonlinear reaction-diffusion equations—II. Steady state solutions and comparison with numerical simulations

1975 • 112 citations

Multiplicity, Stability, and Sensitivity of States in Chemically Reacting Systems—A Review

1975 • 111 citations

Pacemaker activity during aggregation in Dictyostelium discoideum

1974 • 109 citations

Chemical Turbulence: Chaos in a Simple Reaction-Diffusion System

1976 • 108 citations

Signal emission and signal propagation during early aggregation in Dictyostelium discoideum

1976 • 108 citations

Chaos in abstract kinetics: Two prototypes

1977 • 107 citations

Patterns of Spatiotemporal Organization in an Allosteric Enzyme Model

1973 • 103 citations

Bifurcation analysis of nonlinear reaction-diffusion equations—II. Steady state solutions and comparison with numerical simulations

1975 • 95 citations

Non-linear aspects of dynamic pattern in cellular networks

1974 • 94 citations

The Existence of Oscillatory Solutions in the Field–Noyes Model for the Belousov–Zhabotinskii Reaction

1975 • 91 citations

Analytic representation of oscillations, excitability, and traveling waves in a realistic model of the Belousov–Zhabotinskii reaction

1977 • 90 citations

Horizontal Bands in the Belousov Reaction

1973 • 89 citations

Axiomatic Treatment of Chemical Reaction Systems

1962 • 89 citations

Spatial periodic homogeneous chemical reaction

1969 • 87 citations

Dictyostelium discoideum aggregation fields as excitable media

1973 • 86 citations

Chaos in the Zhabotinskii reaction

1978 • 81 citations

On travelling wave solutions in a model for the Belousov-Zhabotinskii reaction

1976 • 81 citations

Electrical stimulation of gastric electrical control activity

1973 • 80 citations

Pattern Formation in Oscillatory Chemical Reactions

1976 • 79 citations

Mechanism for oscillatory synthesis of cyclic AMP in Dictyostelium discoideum

1975 • 76 citations

Local Structures in Chemical Reactions with Heterogeneous Catalysis

1972 • 76 citations

Computer simulation of intestinal slow-wave frequency gradient

1970 • 73 citations

Three steady state situation in an open chemical reaction system. I

1977 • 73 citations

Nerve conduction theory: Some mathematical consequences of Bernstein's model

1940 • 69 citations

Stadienspezifische Aggregationsmuster beiDictyostelium discoideum

1965 • 67 citations

Surface thermodynamics

1977 • 64 citations

Two kinds of wave in an oscillating chemical solution

1974 • 61 citations

A biochemical model of the circadian clock

1975 • 57 citations

Compound III kinetics and chemiluminescence in oscillatory oxidation reactions catalyzed by horseradish peroxidase

1969 • 56 citations

The Belousov—Zhabotinskii reaction in a continuous flow reactor

1976 • 55 citations

Nerve conduction theory: Some mathematical consequences of Bernstein's model

1940 • 55 citations

[Mechanism of formation of closed propagation pathways in excitable media].

1972 • 55 citations

The effect of duodenal and mid small bowel transection on the frequency gradient of the pacesetter potential in the canine small intestine

1970 • 53 citations

The stability of entrainment conditions for coupled van der pol oscillators used as a model for intestinal electrical rhythms

1977 • 49 citations

Rotating waves as asymptotic solutions of a model chemical reaction

1977 • 49 citations

Computer simulation of reverberating spreading depression in a network of cell automata

1975 • 48 citations

Effects of partial cuts on gastric electrical control activity and its computer model

1972 • 45 citations

Analysis of the conditions causing the oscillatory oxidation of reduced nicotinamide-adenine dinucleotide by horseradish peroxidase

1967 • 44 citations

Optimum topographical conditions for reverberating cortical spreading depression in rats

1974 • 43 citations

Ferroin-Collodion Membranes: Dynamic Concentration Patterns in Planar Membranes

1973 • 42 citations

On the Path of the Excitation Wave in Atrial Flutter

1968 • 42 citations

Electrical activity of small intestinal smooth muscle and its temperature dependence

1975 • 41 citations

Spatial stability of traveling wave solutions of a nerve conduction equation

1975 • 39 citations

Periodic Solutions to Reaction-Diffusion Equations

1976 • 38 citations

[Some regimes of excitation movement in ideal excitable tissue].

1965 • 38 citations

Catastrophe and propagation in chemical reactions

1977 • 35 citations

The dynamics of cellular differentiation and associated pattern formation

1972 • 33 citations

Kinetic feedback processes in physico-chemical oscillatory systems

1974 • 33 citations

Sustained oscillations and threshold phenomena in an operon control circuit

1976 • 33 citations

Stability of the bromate–cerium–malonic acid network. I. Theoretical formulation

1976 • 32 citations

A model for oscillatory kinetic systems

1974 • 32 citations

Theory of oscillations in peroxidase catalyzed oxidation reactions in open system

1969 • 28 citations

Shock Excited Systems as Models for Biological Rhythms

1960 • 27 citations

Limit cycle oscillations in compartmental chemical systems

1974 • 26 citations

Dissipative structures in chemical oscillations with concentrations-dependent frequency

1973 • 25 citations

“Spatial Oscillations” in the Zhabotinskii Reaction

1973 • 25 citations

AN EXPERIMENTAL STUDY OF CHEMICAL WAVE PROPAGATION

1973 • 24 citations

Propagation and electrical entrainment of intestinal slow waves

1972 • 24 citations

Dissipative structures in two dimensions

1975 • 24 citations

Neutrally stable traveling wave solutions of nerve conduction equations

1975 • 22 citations

Spatial instability in simple reaction schemes

1975 • 21 citations

The Amplification Before Decay of Perturbations Around Stable States in a Model of the Zhabotinskii Reaction

1977 • 21 citations

Intestinal slow waves: Decrease in propagation velocity along upper small intestine

1969 • 21 citations

Spiral Waves in a Nonlinear Dissipative System

1976 • 20 citations

Temporal and Spatial Structures in Chemical Instabilities

1976 • 20 citations

A principle for chemical multivibration

1972 • 19 citations

Spatial Effects in Active Chemical Systems. I. Model of Leading Center

1977 • 18 citations

Das Experiment: Eine oszillierende Reaktion

1973 • 18 citations

The malignant transformation as a metabolic steady state transition: The possible significance of the phasing of enzyme synthesis and related aspects

1973 • 17 citations

On the temporal characteristics of a model for the Zhabotinskii-Belousov reaction

1975 • 15 citations

Clocklike behaviour of biological clocks

1976 • 13 citations

Excitable chemical reaction systems I. Definition of excitability and simulation of model systems

1975 • 13 citations

The Instability of Evolving Systems

1977 • 13 citations

[2 alternative autooscillatory stationary states in thiol metabolism--2 alternative types of cell multiplication: normal and neoplastic].

1970 • 12 citations

Local phase and renormalized frequency in inhomogeneous chemioscillations

1976 • 12 citations

Effects of transection on small intestinal slow-wave propagation velocity

1973 • 11 citations

Critical Length of the Transport-Dominated Region for Oscillating Non-Linear Reactive Processes

1974 • 11 citations

Validity of the weak diffusion expansion for solutions to systems of reaction-diffusion equations

1975 • 10 citations

Chemical hysteresis, a new type of behavior in the Belousov-Zhabotinskii reaction

1976 • 9 citations

[l model of a leading center].

1975 • 9 citations

[Vagus inhibition--cause of the formation of closed pathways of excitation conduction in auricles].

1970 • 8 citations

Asymptotic Solutions of the Field‐Noyes Model for the Belousov Reaction—I. Homogeneous Oscillations

1976 • 7 citations

[Propagation of impulses in the circuit of excitable tissue].

1965 • 6 citations

Periodic Plane Waves for the Oregonator

1976 • 5 citations

[Instability and excitation propagation in a catalytic reaction model. II. Distributed system model].

1975 • 3 citations

The disappearance of solitary traveling wave solutions of a model of the belousov-zhabotinskii reaction

1977 • 3 citations

One dimensional periodic structures in space and time

1975 • 3 citations

Intrinsic critical length associated with oscillatory reactive processes in complex solutions: Hydrodynamic estimates

1977 • 3 citations

PERIODIC TRANSFORMATION OF THE NERVE FIBER RHYTHM WITH GRADUALLY CHANGING PROPERTIES

1964 • 3 citations

Asymptotic Solutions of the Field‐Noyes Model for the Belousov Reaction—II. Plane Waves

1976 • 1 citations