Competitive modes for the Baier-Sahle hyperchaotic flow in arbitrary dimensions

    Authors

    H. S. Nik;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Nonlinear Dyn.

    Keywords

    Nonlinear dynamics; Hyperchaotic system; Competitive modes; Baier-Sahle; hyperchaotic flow; CHAOS SYNCHRONIZATION; ANTI-SYNCHRONIZATION; LORENZ; ATTRACTORS; DESIGN; SYSTEM; Engineering, Mechanical; Mechanics

    Abstract

    The method of competitive modes has been applied in the literature in order to determine if a given dynamical system exhibits chaos, and can be viewed as providing a sort of necessary condition for the occurrence of chaos. In this way, the method has been used as a diagnostic tool in order to determine parameter regimes for which a certain nonlinear system could exhibit chaos. Presently, we apply the method in order to study the N-dimensional Baier-Sahle hyperchaotic flow. This model is a natural choice, since it is a prototypical model of hyperchaos, yet it is simple enough to be analytically tractable. For the N-dimensional model, we show the existence of up to N-1 competitive modes in the presence of hyperchaos. Interestingly, only two of the mode frequencies are time-variable. So, the Baier-Sahle hyperchaotic flow is an example of a fairly simple high-dimensional hyperchaotic model, which lends itself nicely to a competitive modes analysis. Explicit numerical results are provided for the N=4 and N=5 cases in order to better illustrate our results.

    Journal Title

    Nonlinear Dynamics

    Volume

    74

    Issue/Number

    3

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    581

    Last Page

    590

    WOS Identifier

    WOS:000325824900008

    ISSN

    0924-090X

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