Perturbation methods, bifurcation theory and computer algebra

Computer Algebra in Systems Theory

Galois Theory, Splitting Fields, and Computer Algebra

We provide some algorithms for dynamically obtaining both a possible representation of the splitting field and the Galois group of a given separable polynomial from its universal decomposition algebra. c © 2006 Elsevier Ltd. All rights reserved.

Lattice Perturbation Theory by Computer Algebra : A Three - Loop Result for the Topological Susceptibility

We present a scheme for the analytic computation of renormalization functions on the lattice, using a symbolic manipulation computer language. Our first nontrivial application is a new three-loop result for the topological susceptibility.

Perturbation Methods for Bifurcation Analysis from Multiple Nonresonant Complex Eigenvalues

It is shown that the logical bases of the static perturbation method, which is currently used in static bifurcation analysis, can also be applied to dynamic bifurcations. A two-time version of the Lindstedt–Poincaré Method and the Multiple Scale Method are employed to analyze a bifurcation problem of codimension two. It is found that the Multiple Scale Method furnishes, in a straightforward way...

Quasi-Steady State - Intuition, Perturbation Theory and Algorithmic Algebra

This survey of mathematical approaches to quasi-steady state (QSS) phenomena provides an analytical foundation for an algorithmicalgebraic treatment of the associated (parameter-dependent) ordinary differential systems, in particular for reaction networks. Topics include an ad hoc reduction procedure, singular perturbations, and methods to identify suitable parameter regions. MSC (2010): 92C45,...