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Difficulties in detecting chaos in a complex system

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  • Petkov, Boyan H.

Abstract

The sequences, given by a 7D map, are analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system, determined by comparatively high number of parameters. The same diagnostic approaches are applied to the 3D Lorenz map for comparison. The results show that for some of the sequences yielded from the 7D map, the adopted methods are not able to give a straightforward answer to the question if the system is chaotic as in the 3D case. Since the sequences, subject to the analysis, are not contaminated by noise and are sufficiently long, it could be assumed that such difficulties arise likely due to specific internal features of the more complex system. It is found also that an increase from 0.01 to 0.5 of the sampling step, determining the sequences obtained from the 7D map, masks the chaos in some of them.

Suggested Citation

  • Petkov, Boyan H., 2015. "Difficulties in detecting chaos in a complex system," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 35-47.
    • Handle: RePEc:eee:apmaco:v:260:y:2015:i:c:p:35-47
    DOI: 10.1016/j.amc.2015.03.034
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    References listed on IDEAS

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    1. Awrejcewicz, J. & Krysko, A.V. & Papkova, I.V. & Krysko, V.A., 2012. "Routes to chaos in continuous mechanical systems. Part 3: The Lyapunov exponents, hyper, hyper-hyper and spatial–temporal chaos," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 721-736.
    2. Krysko, A.V. & Awrejcewicz, J. & Papkova, I.V. & Krysko, V.A., 2012. "Routes to chaos in continuous mechanical systems: Part 2. Modelling transitions from regular to chaotic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 709-720.
    3. Awrejcewicz, J. & Krysko, V.A. & Papkova, I.V. & Krysko, A.V., 2012. "Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 687-708.
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