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REGULAR AND CHAOTIC DYNAMICS OF THE LORENZ–STENFLO SYSTEM

JOÃO C. XAVIER

Departamento de Física, Universidade do Estado de Santa Catarina, 89223-100 Joinville, Brazil

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and

PAULO C. RECH

Departamento de Física, Universidade do Estado de Santa Catarina, 89223-100 Joinville, Brazil

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https://doi.org/10.1142/S0218127410025466Cited by:23 (Source: Crossref)

Abstract

We analytically investigate the dynamics of the generalized Lorenz equations obtained by Stenflo for acoustic gravity waves. By using Descartes' Rule of Signs and Routh–Hurwitz Test, we decide on the stability of the fixed points of the Lorenz–Stenflo system, although without explicit solution of the eigenvalue equation. We determine the precise location where pitchfork and Hopf bifurcation of fixed points occur, as a function of the parameters of the system. Parameter-space plots, Lyapunov exponents, and bifurcation diagrams are used to numerically characterize periodic and chaotic attractors.

Keywords:

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