Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in ODEs
Yu.A. Kuznetsov, H.G.E. Meijer, W. Govaerts, B. Sautois
TL;DR
This paper develops algorithms for transitioning from codimension 2 equilibrium bifurcations to codimension 1 cycle bifurcations in high-dimensional ODEs, with implementation details and applications to complex models.
Contribution
It introduces a comprehensive algorithmic framework for switching to cycle bifurcations from codim 2 equilibrium bifurcations, including implementation and performance analysis.
Findings
Successful application to Lorenz-84 model and laser system
Efficient algorithmic implementation demonstrated
Enhanced understanding of bifurcation structures in high-dimensional systems
Abstract
The paper provides full algorithmic details on switching to the continuation of all possible codim 1 cycle bifurcations from generic codim 2 equilibrium bifurcation points in n-dimensional ODEs. We discuss the implementation and the performance of the algorithm in several examples, including an extended Lorenz-84 model and a laser system.
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