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Existence and Stability of Multiple Impulse Solutions of a Nerve Equation

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What this work says

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

inferredcites →https://doi.org/10.1016/0001-8708(70)90023-xopenalex-snapshot
Nagumo's equation
inferredcites →https://doi.org/10.1016/0022-0396(77)90116-4openalex-snapshot
A geometric approach to singular perturbation problems with applications to nerve impulse equations
inferredcites →https://doi.org/10.1016/0025-5564(77)90076-1openalex-snapshot
Local stability of the nerve impulse
inferredcites →https://doi.org/10.1016/s0006-3495(61)86902-6openalex-snapshot
Impulses and Physiological States in Theoretical Models of Nerve Membrane
inferredcites →https://doi.org/10.1016/s0006-3495(73)86065-5openalex-snapshot
Traveling Wave Solutions of a Nerve Conduction Equation
inferredcites →https://doi.org/10.1016/s0006-3495(78)85511-8openalex-snapshot
Temporal stability of solitary impulse solutions of a nerve equation
inferredcites →https://doi.org/10.1080/00029890.1975.11993972openalex-snapshot
Some Mathematical Problems from Neurobiology
inferredcites →https://doi.org/10.1109/jrproc.1962.288235openalex-snapshot
An Active Pulse Transmission Line Simulating Nerve Axon
inferredcites →https://doi.org/10.1113/jphysiol.1952.sp004764openalex-snapshot
A quantitative description of membrane current and its application to conduction and excitation in nerve
inferredcites →https://doi.org/10.1137/0136027openalex-snapshot
Bursting Phenomena in Excitable Membranes
inferredcites →https://doi.org/10.1137/0142016openalex-snapshot
Double Impulse Solutions in Nerve Axon Equations
inferredcites →https://doi.org/10.1137/0142018openalex-snapshot
Single and Multiple Pulse Waves for the FitzHugh–Nagumo
inferredcites →https://doi.org/10.1512/iumj.1972.21.21071openalex-snapshot
inferredcites →https://doi.org/10.1512/iumj.1972.22.22009openalex-snapshot
inferredcites →https://doi.org/10.1512/iumj.1972.22.22048openalex-snapshot
inferredcites →https://doi.org/10.1512/iumj.1975.24.24096openalex-snapshot

What points at this work

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

inferred← citeshttps://doi.org/10.1002/cpa.3160410106openalex-snapshot
Multiple impulse solutions to McKean's caricature of the nerve equation. I—existence
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Multiple impulse solutions to McKean's caricature of the nerve equation. II. Stability
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Variations in interpulse interval of double action potentials during propagation in single neurons
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Propagating Action Potentials
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Traveling Waves with Finitely Many Pulses in a Nerve Equation
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Traveling pulses in a two-component active medium with diffusion
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Homoclinic bifurcation at resonant eigenvalues
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N-Homoclinic bifurcations for homoclinic orbits changing their twisting
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On a stability property of double-pulse solutions in nerve axon equations
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Global Mild Solutions for a Nonautonomous 2D Navier–Stokes Equations with Impulses at Variable Times
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Separating Dissipative Pulses: The Exit Manifold
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Chaos control in the fractional order logistic map via impulses
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Branching of double pulse solutions from single pulse solutions in nerve axon equations
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Traveling waves of infinitely many pulses in nerve equations
inferred← citeshttps://doi.org/10.1016/0025-5564(82)90074-8openalex-snapshot
Heteroclinic waves of the FitzHugh-Nagumo equations
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Homoclinic orbits in a parametrized saddle-focus system
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A spike train with a step change in the interspike intervals in the FitzHugh-Nagumo model
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Chaotic wavetrains in a nerve conduction model
inferred← citeshttps://doi.org/10.1016/0375-9601(85)90854-0openalex-snapshot
Multiple pulse homoclinic orbits in a nerve conduction equation
inferred← citeshttps://doi.org/10.1016/0375-9601(87)90488-9openalex-snapshot
Travelling wave solutions near isolated double-pulse solitary waves of nerve axon equations
inferred← citeshttps://doi.org/10.1016/0375-9601(92)90160-nopenalex-snapshot
The stability of homoclinic pulses: a generalisation of Evans's method
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Existence and stability of traveling pulse solutions of the FitzHugh–Nagumo equation
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Anisotropy, propagation failure, and wave speedup in traveling waves of discretizations of a Nagumo PDE
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Traveling waves of calcium in pancreatic acinar cells: model construction and bifurcation analysis
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Exit manifolds for lattice differential equations
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Stationary bistable pulses in discrete inhomogeneous media
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Propagation failure of fronts in discrete inhomogeneous media with a sawtooth nonlinearity
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Complexity in the bifurcation structure of homoclinic loops to a saddle-focus
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Analysis of Wave Phenomena in a Morphogenetic Mechanochemical Model and an Application to Post-fertilization Waves on Eggs
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Double Impulse Solutions in Nerve Axon Equations
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Single and Multiple Pulse Waves for the FitzHugh–Nagumo
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Existence of Traveling Wave Trains in Nerve Axon Equations
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Stability of Double-Pulse Solutions in Nerve Axon Equations
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Calculation of the Threshold Surface for Nerve Equations
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Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations
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Stability Analysis for the Slow Travelling Pulse of the FitzHugh–Nagumo System
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The Existence of Infinitely Many Traveling Front and Back Waves in the FitzHugh–Nagumo Equations
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Interaction Manifolds for Reaction Diffusion Equations in Two Dimensions
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NEURAL EXCITABILITY, SPIKING AND BURSTING
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A COMPARATIVE STUDY OF THE HODGKIN–HUXLEY AND FITZHUGH–NAGUMO MODELS OF NEURON PULSE PROPAGATION
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UNIFORM ATTRACTORS OF NONAUTONOMOUS DISCRETE REACTION–DIFFUSION SYSTEMS IN WEIGHTED SPACES
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EVANS FUNCTIONS AND BIFURCATIONS OF STANDING WAVE FRONTS OF A NONLINEAR SYSTEM OF REACTION DIFFUSION EQUATIONS
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