Numerical analysis of parametrized nonlinear equations
Numerical analysis of parametrized nonlinear equations
Bifurcations via singular value decompositions
Applied Mathematics and Computation
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms
ACM Transactions on Mathematical Software (TOMS)
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
On Smooth Decompositions of Matrices
SIAM Journal on Matrix Analysis and Applications
A locally parameterized continuation process
ACM Transactions on Mathematical Software (TOMS)
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
ACM Transactions on Mathematical Software (TOMS)
Locating coalescing singular values of large two-parameter matrices
Mathematics and Computers in Simulation
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In this paper, we propose a path-following method for computing a curve of equilibria of a dynamical system, based upon the smooth Singular Value Decomposition (SVD) of the Jacobian matrix. Our method is capable of detecting fold points, and continuing past folds. It is also able to detect branch points and to switch branches at such points. Algorithmic details and examples are given.