Computation and Continuation of Homoclinic and Heteroclinic Orbits with Arclength Parameterization

DOI10.1137/S1064827595288218zbMath0867.34037OpenAlexW2005038693MaRDI QIDQ3124019

Robert D. Russell, Gerald Moore, Lixin Liu

Publication date: 11 August 1997

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s1064827595288218

zbMATH Keywords

collocation methodcontinuationhomoclinic and heteroclinic orbitsnumericalAUTO

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (12)

Free boundary formulation for BVPs on a semi-infinite interval and non-iterative transformation methods ⋮ A new method to find homoclinic and heteroclinic orbits ⋮ Accurate determination of heteroclinic orbits in chaotic dynamical systems ⋮ Finite difference schemes on quasi-uniform grids for BVPs on infinite intervals ⋮ Numerical computation of connecting orbits in planar piecewise smooth dynamical system ⋮ A new approach of asymmetric homoclinic and heteroclinic orbits construction in several typical systems based on the undetermined Padé approximation method ⋮ A variational approach to connecting orbits in nonlinear dynamical systems ⋮ Strongly nonlinear effects on internal solitary waves in three-layer flows ⋮ A free boundary approach and keller's box scheme for BVPs on infinite intervals ⋮ Continuation of limit cycles near saddle homoclinic points using splines in phase space ⋮ Numerical bifurcation analysis for ODEs ⋮ A survey on free boundary identification of the truncated boundary in numerical BVPs on infinite intervals

Uses Software

• AUTO

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