Numerical computation of heteroclinic orbits
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Analysis of neural excitability and oscillations
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Elements of applied bifurcation theory (2nd ed.)
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SIAM Journal on Matrix Analysis and Applications
Numerical methods for bifurcations of dynamical equilibria
Numerical methods for bifurcations of dynamical equilibria
Computing Connecting Orbits via an Improved Algorithm for Continuing Invariant Subspaces
SIAM Journal on Scientific Computing
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
ACM Transactions on Mathematical Software (TOMS)
Continuation of Invariant Subspaces in Large Bifurcation Problems
SIAM Journal on Scientific Computing
Continuation of homoclinic orbits in MATLAB
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
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matcont is a matlab continuation package for the interactive numerical study of a range of parameterized nonlinear dynamical systems, in particular ODEs, that allows to compute curves of equilibria, limit points, Hopf points, limit cycles, flip, fold and torus bifurcation points of limit cycles. It is now possible to continue homoclinic-to-hyperbolic-saddle and homoclinic-to-saddle-node orbits in matcont. The implementation is done using the continuation of invariant subspaces, with the Riccati equations included in the defining system. A key feature is the possibility to initiate both types of homoclinic orbits interactively, starting from an equilibrium point and using a homotopy method. All known codimension-two homoclinic bifurcations are tested for during continuation. The test functions for inclination-flip bifurcations are implemented in a new and more efficient way. Heteroclinic orbits can now also be continued and an analogous homotopy method can be used for the initialization.