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Shil’nikov chaos in the 4D Lorenz-Stenflo system modeling the time evolution of nonlinear acoustic-gravity waves in a rotating atmosphere. (English) Zbl 1284.37022

Summary: The Lorenz-Stenflo system serves as a model of the time evolution of nonlinear acoustic-gravity waves in a rotating atmosphere. In the present paper, we study the Shil’nikov chaos which arises in the 4D Lorenz-Stenflo system. The analytical and numerical results constitute an application of the Shil’nikov theorems to a 4D system (whereas most results present in the literature deal with applying the Shil’nikov theorems to 3D systems), which allows for the study of chaos along homoclinic and heteroclinic orbits arising as solutions to the Lorenz-Stenflo system. We verify the observed chaos via competitive modes analysis – a diagnostic for chaotic systems. We give an analytical test, completely in terms of the model parameters, for the Smale horseshoe chaos near homoclinic orbits of the origin, as well as for the case of specific heteroclinic orbits. Numerical results are shown for other cases in which the general analytical method becomes too complicated to apply. These results can be extended to more complicated higher-dimensional systems governing plasmas, and, in particular, may be used to shed light on period-doubling and Smale horseshoe chaos that arises in such models.

MSC:

37C29 Homoclinic and heteroclinic orbits for dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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