Computational Science – ICCS 2005

Volume 3514 of the series Lecture Notes in Computer Science pp 50-57

Bifurcation Analysis of Large Equilibrium Systems in Matlab

  • David S. BindelAffiliated withDepartment of Electrical Engineering and Computer Science, University of California at Berkeley
  • , James W. DemmelAffiliated withDepartment of Electrical Engineering and Computer Science, Department of Mathematics, University of California at Berkeley
  • , Mark J. FriedmanAffiliated withMathematical Sciences Department, University of Alabama in Huntsville
  • , Willy J. F. GovaertsAffiliated withDepartment of Applied Mathematics and Computer Science, Ghent University
  • , Yuri A. KuznetsovAffiliated withMathematisch Instituut

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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.