Global organization of phase space in the transition to chaos in the Lorenz system

DOI10.1088/0951-7715/28/11/R113zbMath1332.34083OpenAlexW2243481998WikidataQ114476391 ScholiaQ114476391MaRDI QIDQ3458785

Eusebius J. Doedel, Bernd Krauskopf, Hinke M. Osinga

Publication date: 23 December 2015

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/28/11/r113

zbMATH Keywords

global bifurcationsboundary value problem setupglobal invariant manifolds

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Complex behavior and chaotic systems of ordinary differential equations (34C28) Invariant manifolds for ordinary differential equations (34C45) Attractors of solutions to ordinary differential equations (34D45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Numerical problems in dynamical systems (65P99)

Related Items (15)

Computing stable hierarchies of fiber bundles ⋮ Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system ⋮ From wild Lorenz-like to wild Rovella-like dynamics ⋮ Hidden Attractors on One Path: Glukhovsky–Dolzhansky, Lorenz, and Rabinovich Systems ⋮ Finding First Foliation Tangencies in the Lorenz System ⋮ Superluminal periodic orbits in the Lorenz system ⋮ Study of a simple 3D quadratic system with homoclinic flip bifurcations of inward twist case \(\mathbf{C}_{\mathbf{in}}\) ⋮ Bounding extrema over global attractors using polynomial optimisation ⋮ A Conley index study of the evolution of the Lorenz strange set ⋮ On areas of attraction and repulsion in finite time dynamical systems and their numerical approximation ⋮ On conditions for rate-induced tipping in multi-dimensional dynamical systems ⋮ A Lorenz-type attractor in a piecewise-smooth system: Rigorous results ⋮ Sliding homoclinic bifurcations in a Lorenz-type system: Analytic proofs ⋮ Lorenz attractors and the modular surface ^* ⋮ Chaos in the Periodically Parametrically Excited Lorenz System

Uses Software

• AUTO
• AUTO-07P
• COLSYS

Cites Work

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