Bifurcation Analysis of Large Equilibrium Systems in Matlab

  • David S. Bindel
  • James W. Demmel
  • Mark J. Friedman
  • Willy J. F. Govaerts
  • Yuri A. Kuznetsov
Conference paper

DOI: 10.1007/11428831_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3514)
Cite this paper as:
Bindel D.S., Demmel J.W., Friedman M.J., Govaerts W.J.F., Kuznetsov Y.A. (2005) Bifurcation Analysis of Large Equilibrium Systems in Matlab. In: Sunderam V.S., van Albada G.D., Sloot P.M.A., Dongarra J.J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3514. Springer, Berlin, Heidelberg

Abstract

The Continuation of Invariant Subspaces (CIS) algorithm produces a smoothly varying basis for an invariant subspace \(\mathcal{R}(s)\) of a parameter-dependent matrix A(s). In the case when A(s) is the Jacobian matrix for a system that comes from a spatial discretization of a partial differential equation, it will typically be large and sparse. Cl_matcont is a user-friendly matlab package for the study of dynamical systems and their bifurcations. We incorporate the CIS algorithm into cl_atcont to extend its functionality to large scale bifurcation computations via subspace reduction.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • David S. Bindel
    • 1
  • James W. Demmel
    • 2
  • Mark J. Friedman
    • 3
  • Willy J. F. Govaerts
    • 4
  • Yuri A. Kuznetsov
    • 5
  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of California at BerkeleyBerkeley
  2. 2.Department of Electrical Engineering and Computer Science, Department of MathematicsUniversity of California at BerkeleyBerkeley
  3. 3.Mathematical Sciences DepartmentUniversity of Alabama in HuntsvilleHuntsville
  4. 4.Department of Applied Mathematics and Computer ScienceGhent UniversityGhentBelgium
  5. 5.Mathematisch InstituutUtrechtThe Netherlands

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