Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Numerical methods for bifurcations of dynamical equilibria
Numerical methods for bifurcations of dynamical equilibria
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics
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CL_MATCONT is a Matlab continuation package for the numerical study of a range of parameterized nonlinear problems. In the case of ODEs it allows to compute curves of equilibria, limit point, Hopf points, limit cycles and period doubling bifurcation points of limit cycles. All curves are computed by the same function that implements a prediction-correction continuation algorithm based on the Moore - Penrose matrix pseudo-inverse. The continuation of bifurcation points of equilibria and limit cycles is based on bordering methods and minimally extended systems. Hence no additional unknowns such as singular vectors and eigenvectors are used and no artificial sparsity in the systems is created.The inherent sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods.CL_MATCONT furthermore allows to compute solution branches to underdetermined systems of nonlinear equations and parameterized boundary value problems.