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Periodic Orbit Continuation in Multiple Time Scale Systems

  • John Guckenheimer
  • M Drew LaMar
Chapter
Part of the Understanding Complex Systems book series (UCS)

Continuation methods utilizing boundary value solvers are an effective tool for computing unstable periodic orbits of dynamical systems. Auto [7] is the standard implementation of these procedures. Unfortunately, the collocation methods used in Auto often require very fine meshes for convergence on problems with multiple time scales. This inconvenience prompts the search for alternative methods for computing such periodic orbits; we introduce here new multiple-shooting algorithms based on geometric singular perturbation theory.

Keywords

Periodic Orbit Hopf Bifurcation Multiple Time Scale Critical Manifold Geometric Singular Perturbation Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Canopus Publishing Limited 2007

Authors and Affiliations

  • John Guckenheimer
    • 1
  • M Drew LaMar
    • 1
  1. 1.Mathematics DepartmentCornell UniversityUSA

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