Perturbed bifurcation theory

Perturbed period-doubling bifurcation. I. Theory.

Stochastic Global Bifurcation in Perturbed Hamiltonian Systems

We study two perturbed Hamiltonian systems in which chaos-like dynamics can be induced by stochastic perturbations. We show the similarities of a class of population and laser models, analytically and topologically. Both systems have similar manifold structure that includes bi-instability and partially formed heteroclinic connections. Noise takes advantage of this structure, inducing a global b...

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...

Introduction to bifurcation theory

The theory of bifuxcation from equilibria based on center-manifold reduction and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail:...

Perturbed period-doubling bifurcation. II. Experiments on Josephson junctions.