Numerical bifurcation analysis for ODEs

Numerical Analysis for Nonlinear and Bifurcation Problems

PREFACE Computational applications generally involve nonlinear problems and often contain parameters. They may represent properties of the physical system they describe or quantities which can be varied. A basic problem in approximation consists in studying existence and convergence of approximated solutions for a given nonlinear problem, for instance when the parameters are xed. Another proble...

Numerical Bifurcation For

A case study for homoclinic chaos in an autonomous electronic circuit: A trip from Takens-Bogdanov to Hopf-Shilnikov.

Multirate Numerical Integration for Stiff ODEs

This paper contains an overview of a self-adjusting multirate method. A simple extension which allows the improvement of the efficiency of the method is introduced. The performance of the extended and the original method is compared for a test problem.

Numerical Bifurcation Analysis of Dynamical Systems

Numerical Analysis of Perturbed Bifurcation Problems

Perturbations of nonlinear equations exhibiting bifurcation from simple eigenvalue can either preserve or destroy the bifurcation. Both types of perturbation are investigated, and some numerical techniques suited for the determination of the associated solution manifold are proposed. These methods can be implemented into existing software packages of numerical standard algorithms for path-follo...