Hybrid projective synchronization and control of the Baier-Sahle hyperchaotic flow in arbitrary dimensions with unknown parameters

    Authors

    H. S. Nik; J. Saberi-Nadjafi; S. Effati;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Appl. Math. Comput.

    Keywords

    Hyperchaos control; Hybrid projective synchronization; Nonlinear; feedback controller; Lasalle invariance principle; CHAOTIC SYSTEMS; ANTI-SYNCHRONIZATION; COMPETITIVE MODES; LORENZ; DESIGN; NETWORKS; ORDER; Mathematics, Applied

    Abstract

    The problem of hybrid projective synchronization (HPS) strategies and control for the Baier-Sahle hyperchaotic flow in arbitrary dimensions with unknown parameters is considered. Based on the Lasalle invariance principle and adaptive control method, adaptive controllers and parameters update laws are given for the HPS between two identical hyper-chaotic systems with fully unknown parameters. Using this method, the Baier-Sahle hyperchaotic flow in arbitrary dimensions is controlled to the unsteady equilibrium points. The Baier-Sahle hyperchaotic flow is a useful choice for this analysis, since it is a standard model of hyperchaos, yet it is simple enough to be analytically tractable. In particular, the Baier-Sahle hyperchaotic flow has been proposed as an N dimensional nonlinear system model giving the maximal number of positive Lyapunov exponents (N = 2). Both a rigorous theoretical analysis and direct numerical simulations are provided to demonstrate the control of hyperchaos in this model. The results suggest that the methods used here can be applied to more complicated models from which hyperchaos arises. (C) 2014 Elsevier Inc. All rights reserved.

    Journal Title

    Applied Mathematics and Computation

    Volume

    248

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    55

    Last Page

    69

    WOS Identifier

    WOS:000345124800007

    ISSN

    0096-3003

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