Regular and Chaotic Dynamics of the Lorenz-Stenflo System

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.

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