GLOBAL DYNAMICS OF THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES-Reference-Cited by-同舟云学术

GLOBAL DYNAMICS OF THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES

Published:2010-10 Issue:10 Volume:20 Page:3137-3155
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

LLIBRE JAUME¹,MESSIAS MARCELO²,DA SILVA PAULO RICARDO³

Affiliation:

1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain

2. Departamento de Matemática, Estatística e Computação, Faculdade de Ciências e Tecnologia, UNESP – Univ Estadual Paulista, Cx. Postal 266, 19060-900, Presidente Prudente, São Paulo, Brazil

3. Departamento de Matemática, Instituto de Biociências, Letras e Ciências Exatas, UNESP – Univ Estadual Paulista, Rua C. Colombo, 2265, 15054–000, S. J. Rio Preto, São Paulo, Brazil

Abstract

In this paper by using the Poincaré compactification of ℝ3 we describe the global dynamics of the Lorenz system [Formula: see text] having some invariant algebraic surfaces. Of course (x, y, z) ∈ ℝ3 are the state variables and (s, r, b) ∈ ℝ3 are the parameters. For six sets of the parameter values, the Lorenz system has invariant algebraic surfaces. For these six sets, we provide the global phase portrait of the system in the Poincaré ball (i.e. in the compactification of ℝ3 with the sphere 𝕊2 of the infinity).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127410027593

Reference14 articles.

1. Bounded polynomial vector fields

2. Global bifurcations of the Lorenz manifold

3. Two-dimensional global manifolds of vector fields

4. Computing Geodesic Level Sets on Global (Un)stable Manifolds of Vector Fields

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