GLOBAL DYNAMICS of THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES
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Data
2010-10-01
Autores
Llibre, Jaume
Messias, Marcelo [UNESP]
Da Silva, Paulo Ricardo [UNESP]
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Editor
World Scientific Publ Co Pte Ltd
Resumo
In this paper by using the Poincare compactification of R(3) we describe the global dynamics of the Lorenz system(x) over dot = s(-x + y), (y) over dot = rx - y - xz, (z) over dot = -bz + xy,having some invariant algebraic surfaces. of course ( x, y, z) is an element of R(3) are the state variables and (s, r, b) is an element of R(3) 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 Poincare ball (i.e. in the compactification of R(3) with the sphere S(2) of the infinity).
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Palavras-chave
Integrability, Lorenz system, Poincare compactification, dynamics at infinity invariant algebraic surface
Como citar
International Journal of Bifurcation and Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 20, n. 10, p. 3137-3155, 2010.