Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two

DOI10.1080/02681119608806230zbMath0867.34036OpenAlexW1975975592MaRDI QIDQ3128231

Feng-Shan Bai, Alan R. Champneys

Publication date: 11 August 1997

Published in: Dynamics and Stability of Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02681119608806230

zbMATH Keywords

numerical continuationsaddle-node equilibriumhomoclinic orbitsAUTOtruncated boundary-value method

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Bifurcations of Two-Dimensional Global Invariant Manifolds near a Noncentral Saddle-Node Homoclinic Orbit ⋮ \(n\)-dimensional stable and unstable manifolds of hyperbolic singular point

Uses Software

• AUTO
• HomCont

Cites Work

• Homoclinic orbits in a simple chemical model of an autocatalytic reaction
• Numerical analysis and accurate computation of heteroclinic orbits in the case of center manifolds
• Qualitative investigation of a particular nonlinear system
• On the nonlocal application of the method of small parameter
• Numerical Computation of Saddle-Node Homoclinic Bifurcation Points
• Cubic Lienard equations with linear damping
• Homoclinic Bifurcations with Nonhyperbolic Equilibria
• The Numerical Computation of Connecting Orbits in Dynamical Systems
• The Saddle-Node Separatrix-Loop Bifurcation
• Numerical Computation and Continuation of Invariant Manifolds Connecting Fixed Points
• Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point
• Rate of convergence of numerical approximations to homoclinic bifurcation points
• NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
• A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS
• TRAVELLING WAVES WITH SPATIALLY RESONANT FORCING: BIFURCATIONS OF A MODIFIED LANDAU EQUATION
• A non-transverse homoclinic orbit to a saddle-node equilibrium

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