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Regular and chaotic dynamics of the Lorenz-Stenflo system. (English) Zbl 1183.34065
Summary: 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.

MSC:
34C60Qualitative investigation and simulation of models (ODE)
34D20Stability of ODE
34C23Bifurcation (ODE)
34C28Complex behavior, chaotic systems (ODE)
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