scholarly journals Dynamical Model Reduction Method for Solving Parameter-Dependent Dynamical Systems

2017 ◽  
Vol 39 (4) ◽  
pp. A1766-A1792 ◽  
Author(s):  
Marie Billaud-Friess ◽  
Anthony Nouy
Keyword(s):  
Dynamical Systems ◽  
Model Reduction ◽  
Reduction Method ◽  
Dynamical Model ◽  
Parameter Dependent

A new model reduction method for nonlinear dynamical systems

2009 ◽  
Vol 59 (1-2) ◽  
pp. 183-194 ◽  
Author(s):  
Nikolaos Kazantzis ◽  
Costas Kravaris ◽  
Lemonia Syrou
Keyword(s):  
Dynamical Systems ◽  
Model Reduction ◽  
Reduction Method ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
New Model

ON THE LOCATION AND CONTINUATION OF HOPF BIFURCATIONS IN LARGE-SCALE PROBLEMS

2008 ◽  
Vol 18 (05) ◽  
pp. 1589-1597 ◽  
Author(s):  
M. FRIEDMAN ◽  
W. QIU
Keyword(s):  
Dynamical Systems ◽  
Large Scale ◽  
Orthonormal Basis ◽  
Invariant Subspaces ◽  
Hopf Bifurcations ◽  
Augmented System ◽  
Large Scale Problems ◽  
System Technique ◽  
Matlab Package ◽  
Parameter Dependent

CL_MATCONT is a MATLAB package for the study of dynamical systems and their bifurcations. It uses a minimally augmented system for continuation of the Hopf curve. The Continuation of Invariant Subspaces (CIS) algorithm produces a smooth orthonormal basis for an invariant subspace [Formula: see text] of a parameter-dependent matrix A(s). We extend a minimally augmented system technique for location and continuation of Hopf bifurcations to large-scale problems using the CIS algorithm, which has been incorporated into CL_MATCONT. We compare this approach with using a standard augmented system and show that a minimally augmented system technique is more suitable for large-scale problems. We also suggest an improvement of a minimally augmented system technique for the case of the torus continuation.

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