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Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study

https://doi.org/10.1007/bf01063734
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What this work says

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

inferredcites →https://doi.org/10.1007/978-1-4612-5929-9openalex-snapshot
Applications of Centre Manifold Theory
inferredcites →https://doi.org/10.1007/978-94-009-0659-4_11openalex-snapshot
Global Bifurcations and their Numerical Computation
inferredcites →https://doi.org/10.1007/978-94-009-0659-4_13openalex-snapshot
A Method for Homoclinic and Heteroclinic Continuation in Two and Three Dimensions
inferredcites →https://doi.org/10.1007/bf01063735openalex-snapshot
Numerical analysis and accurate computation of heteroclinic orbits in the case of center manifolds
inferredcites →https://doi.org/10.1016/0377-0427(89)90153-2openalex-snapshot
Numerical computation of heteroclinic orbits
inferredcites →https://doi.org/10.1017/s0308210500031528openalex-snapshot
Using Melnikov's method to solve Silnikov's problems
inferredcites →https://doi.org/10.1063/1.2811021openalex-snapshot
Chaotic Vibrations: An Introduction for Applied Scientists and Engineers
inferredcites →https://doi.org/10.1093/imanum/10.3.379openalex-snapshot
The Numerical Computation of Connecting Orbits in Dynamical Systems
inferredcites →https://doi.org/10.1093/oso/9780198556466.001.0001openalex-snapshot
Chemical Oscillations and Instabilities
inferredcites →https://doi.org/10.1115/1.3157655openalex-snapshot
New Approaches to Nonlinear Problems in Dynamics
inferredcites →https://doi.org/10.1115/1.3173762openalex-snapshot
Chaotic Vibrations: An Introduction for Applied Scientists and Engineers
inferredcites →https://doi.org/10.1137/0518083openalex-snapshot
The Saddle-Node Separatrix-Loop Bifurcation
inferredcites →https://doi.org/10.1137/0728042openalex-snapshot
Numerical Computation and Continuation of Invariant Manifolds Connecting Fixed Points
inferredcites →https://doi.org/10.1137/0730060openalex-snapshot
Numerical Computation of Saddle-Node Homoclinic Bifurcation Points
inferredcites →https://doi.org/10.57262/die/1371571144openalex-snapshot
Bifurcation of a homoclinic orbit with a saddle-node equilibrium

What points at this work

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

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Computer Assisted Proofs for Transverse Collision and Near Collision Orbits in the Restricted Three Body Problem
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Numerical Analysis of Bifurcations
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Dynamical Systems: Some Computational Problems
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Numerical analysis and accurate computation of heteroclinic orbits in the case of center manifolds
inferred← citeshttps://doi.org/10.1007/s10543-015-0567-8openalex-snapshot
Nonautonomous systems with transversal homoclinic structures under discretization
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Critical homoclinics in a restricted four-body problem: numerical continuation and center manifold computations
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Parameterization of Invariant Manifolds for Periodic Orbits (II): A Posteriori Analysis and Computer Assisted Error Bounds
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On locating connecting orbits
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Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem
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Numerical computation of connecting orbits in planar piecewise smooth dynamical system
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[32] Applying bifurcation theory to enzyme kinetics
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A survey on free boundary identification of the truncated boundary in numerical BVPs on infinite intervals
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Homoclinic Twist Bifurcation in a System of Two Coupled Oscillators
inferred← citeshttps://doi.org/10.1023/a:1014917324652openalex-snapshot
T-Points in a Z2-Symmetric Electronic Oscillator. (I) Analysis
inferred← citeshttps://doi.org/10.1023/a:1019152611342openalex-snapshot
Successive continuation for locating connecting orbits
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A free boundary approach and keller's box scheme for BVPs on infinite intervals
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Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two
inferred← citeshttps://doi.org/10.1088/0951-7715/21/8/001openalex-snapshot
A Lin's method approach to finding and continuing heteroclinic connections involving periodic orbits
inferred← citeshttps://doi.org/10.1090/psapm/074/00642openalex-snapshot
Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits
inferred← citeshttps://doi.org/10.1137/0730060openalex-snapshot
Numerical Computation of Saddle-Node Homoclinic Bifurcation Points
inferred← citeshttps://doi.org/10.1137/100812008openalex-snapshot
Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray–Scott Equation
inferred← citeshttps://doi.org/10.1137/120901271openalex-snapshot
A Homoclinic Orbit in a Planar Singular ODE---A Computer Assisted Proof
inferred← citeshttps://doi.org/10.1137/140960207openalex-snapshot
Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form
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Connecting Orbits for Compact Infinite Dimensional Maps: Computer Assisted Proofs of Existence
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Computation and Continuation of Homoclinic and Heteroclinic Orbits with Arclength Parameterization
inferred← citeshttps://doi.org/10.1142/s0218127403008326openalex-snapshot
HOMOCLINIC BRANCH SWITCHING: A NUMERICAL IMPLEMENTATION OF LIN'S METHOD
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NUMERICAL ANALYSIS OF DEGENERATE CONNECTING ORBITS FOR MAPS
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MULTIPARAMETRIC BIFURCATIONS IN AN ENZYME-CATALYZED REACTION MODEL
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Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications
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A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS
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On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup
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Multistage Optimal Parametric Iteration Method Applied to Generate Closed-Form Solutions for Dynamical System with Quadratic Nonlinearities
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How to find a codimension-one heterocliniccycle between two periodic orbits
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Parameterization of slow-stable manifolds and their invariant vector bundles: Theory and numerical implementation
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Computer assisted existence proofs for parameterized cycle-to-cycle connections
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Study of dynamics about and between libration points of Sun-Earth-Moon coherent models
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Algrithm for detecting homoclinic orbits of time-continuous dynamical system and its application
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