Super-Critical and Sub-Critical Hopf bifurcations in two and three dimensions

TL;DR

This paper investigates super-critical and sub-critical Hopf bifurcations in two and three-dimensional systems using renormalization group methods, applying the approach to models like Lorenz and Rössler.

Contribution

It provides a detailed renormalization group analysis of Hopf bifurcations in low-dimensional systems, expanding understanding of bifurcation criteria in these contexts.

Findings

Criteria for Hopf bifurcation occurrence derived

Application to Lorenz and Rössler models demonstrated

Enhanced understanding of bifurcation types in 2D and 3D systems

Abstract

Hopf bifurcations have been studied perturbatively under two broad headings, viz., super-critical and sub-critical. The criteria for occurrences of such bifurcations have been investigated using the renormalization group. The procedure has been described in details for both two and three dimensions and has been applied to several important models, including those by Lorenz and Rossler.