Computing Connecting Orbits via an Improved Algorithm for Continuing Invariant Subspaces

DOI10.1137/S1064827598344868zbMath0967.34008MaRDI QIDQ4509973

Luca Dieci, Mark J. Friedman, James W. Demmel

Publication date: 19 October 2000

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

zbMATH Keywords

bifurcationsinvariant subspacesnumerical continuationconnecting orbits

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Implicit ordinary differential equations, differential-algebraic equations (34A09) Bifurcation theory for ordinary differential equations (34C23) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Orthogonalization in numerical linear algebra (65F25)

Related Items (15)

Numerical computation of the optimal vector field: exemplified by a fishery model ⋮ Continuation of invariant subspaces ⋮ Numerical computation of bifurcations in large equilibrium systems in \textsc{Matlab} ⋮ Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions ⋮ A bisection-like algorithm for branch switching at a simple branch point ⋮ Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values ⋮ ON THE LOCATION AND CONTINUATION OF HOPF BIFURCATIONS IN LARGE-SCALE PROBLEMS ⋮ New features of the software M<scp>at</scp>C<scp>ont</scp>for bifurcation analysis of dynamical systems ⋮ Connecting orbits in perturbed systems ⋮ Efficient computation of analytic bases in Evans function analysis of large systems ⋮ Numerical continuation of connecting orbits of maps in MATLAB ⋮ Initialization of Homoclinic Solutions near Bogdanov--Takens Points: Lindstedt--Poincaré Compared with Regular Perturbation Method ⋮ CONTINUATION OF CONNECTING ORBITS IN 3D-ODEs (II) : CYCLE-TO-CYCLE CONNECTIONS ⋮ Continuous Decompositions and Coalescing Eigenvalues for Matrices Depending on Parameters ⋮ A survey on free boundary identification of the truncated boundary in numerical BVPs on infinite intervals

Uses Software

• HomCont

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