Shil'nikov chaos in the 4D Lorenz-Stenflo system modeling the time evolution of nonlinear acoustic-gravity waves in a rotating atmosphere

    Authors

    R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Nonlinear Dyn.

    Keywords

    Lorenz-Stenflo system; Smale horseshoe chaos; Shil'nikov analysis; PERIODIC-ORBITS; ANTI-SYNCHRONIZATION; HOMOCLINIC ORBITS; COMPETITIVE; MODES; CANONICAL FORM; EQUATIONS; BIFURCATIONS; ATTRACTOR; EXISTENCE; LOOP; Engineering, Mechanical; Mechanics

    Abstract

    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.

    Journal Title

    Nonlinear Dynamics

    Volume

    72

    Issue/Number

    4

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    837

    Last Page

    851

    WOS Identifier

    WOS:000319356200010

    ISSN

    0924-090X

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