NUMERICAL CONTINUATION OF BRANCH POINTS OF EQUILIBRIA AND PERIODIC ORBITS

DOI10.1142/S0218127405012491zbMath1081.37054OpenAlexW2116098329MaRDI QIDQ5318373

Annick Dhooge, W. Kuznetsov, Willy Govaerts, Eusebius J. Doedel

Publication date: 26 September 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127405012491

zbMATH Keywords

periodic orbitslimit cyclesbifurcationsystems with symmetrytest functiongeneric systemsrank defect

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Applications of dynamical systems (37N99) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Periodic orbits of vector fields and flows (37C27) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items

Numerical bifurcation analysis of the bipedal spring-mass model ⋮ Continuation of solutions and studying delay differential equations via rigorous numerics ⋮ ELEMENTAL PERIODIC ORBITS ASSOCIATED WITH THE LIBRATION POINTS IN THE CIRCULAR RESTRICTED 3-BODY PROBLEM ⋮ Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations ⋮ Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator-prey model ⋮ Using Numerical Bifurcation Analysis to Study Pattern Formation in Mussel Beds ⋮ New features of the software M<scp>at</scp>C<scp>ont</scp>for bifurcation analysis of dynamical systems ⋮ A timestepper approach for the systematic bifurcation and stability analysis of polymer extrusion dynamics

Uses Software

• MATCONT
• AUTO2000
• CL_MATCONT
• COLSYS

Cites Work

• Elements of applied bifurcation theory.
• Characterization and Computation of Generalized Turning Points
• Collocation Software for Boundary-Value ODEs
• The numerical treatment of non-trivial bifurcation points
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS
• Computation of Periodic Solution Bifurcations in ODEs Using Bordered Systems
• Numerical Methods for Bifurcations of Dynamical Equilibria
• MATCONT
• Collocation at Gaussian Points