Numerical continuation of homoclinic orbits to non-hyperbolic equilibria in planar systems

DOI10.1023/A:1008367531379zbMath0983.70018MaRDI QIDQ5929819

Emilio Freire, Alejandro J. Rodríguez-Luis, Luis Pizarro

Publication date: 3 April 2002

Published in: Nonlinear Dynamics (Search for Journal in Brave)

zbMATH Keywords

codimension-three homoclinic connectioncodimension-two homoclinic connectioncuspidal loopdegenerate homoclinic orbitdouble-zero eigenvaluenon-hyperbolic equilibriumnumerical continuationsaddle-node equilibriumzero eigenvalue

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44)

Related Items (8)

On the existence of heteroclinic cycles in some class of 3-dimensional piecewise affine systems with two switching planes ⋮ MULTIPARAMETRIC BIFURCATIONS IN AN ENZYME-CATALYZED REACTION MODEL ⋮ Exact Torus Knot Periodic Orbits and Homoclinic Orbits in a Class of Three-Dimensional Flows Generated by a Planar Cubic System ⋮ Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms ⋮ Codimension-3 Bifurcation for Continuous Saddle Bimodal Linear Dynamical Systems ⋮ Convergent analytic solutions for homoclinic orbits in reversible and non-reversible systems ⋮ Analytical approximation of cuspidal loops using a nonlinear time transformation method ⋮ Continuation of limit cycles near saddle homoclinic points using splines in phase space

Uses Software

• PITCON
• HomCont

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