Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Chaotic spikes arising from a model of bursting in excitable membranes
SIAM Journal on Applied Mathematics
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
Computation of Periodic Solution Bifurcations in ODEs Using Bordered Systems
SIAM Journal on Numerical Analysis
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
ACM Transactions on Mathematical Software (TOMS)
Numerical-Symbolic Matlab Program for the Analysis of Three-Dimensional Chaotic Systems
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Neural mass activity, bifurcations, and epilepsy
Neural Computation
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MATCONT is a Matlab continuation package with a GUI for the interactive numerical study of a range of parameterized nonlinear problems. In the case of ODEs it allows to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles and fold bifurcation points of limit cycles. It can use the symbolic toolbox of Matlab to compute derivatives of order up to five of the object function. We discuss some details on the implementation of the limit cycles and the fold bifurcation of limit cycles in MATCONT. The inherent sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by usingthe standard Matlab sparse matrix methods.