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Interval computing periodic orbits of maps using a piecewise approach

Author

Listed:
  • Nepomuceno, Erivelton G.
  • Rodrigues Junior, Heitor M.
  • Martins, Samir A.M.
  • Perc, Matjaž
  • Slavinec, Mitja

Abstract

Interval arithmetic applied to simulation of dynamical systems has attracted a great deal of interest in recent years. Much of this research has been carried out in the calculation of fixed points or low-period windows for nonlinear discrete maps. This study proposes a novel interval computation based on a piecewise method to calculate periodic orbits for the logistic map. Using the cobweb plot, three rounding situations have been applied to a correct outward rounding, as required by interval arithmetic. The proposed method is compared with results in the literature and with the results obtained by means of the Matlab toolbox Intlab. The comparison is accomplished for nine case studies using the logistic map. Numerical results explicitly indicate that the proposed method produces intervals that are substantially narrower than those obtained with the traditional techniques.

Suggested Citation

  • Nepomuceno, Erivelton G. & Rodrigues Junior, Heitor M. & Martins, Samir A.M. & Perc, Matjaž & Slavinec, Mitja, 2018. "Interval computing periodic orbits of maps using a piecewise approach," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 67-75.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:67-75
    DOI: 10.1016/j.amc.2018.04.063
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    References listed on IDEAS

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    1. Nepomuceno, Erivelton G. & Martins, Samir A.M. & Silva, Bruno C. & Amaral, Gleison F.V. & Perc, Matjaž, 2018. "Detecting unreliable computer simulations of recursive functions with interval extensions," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 408-419.
    2. Spandl, Christoph, 2012. "Computational complexity of iterated maps on the interval," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1459-1477.
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    Cited by:

    1. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Aleksandra Tutueva & Timur Karimov & Denis Butusov, 2020. "Semi-Implicit and Semi-Explicit Adams-Bashforth-Moulton Methods," Mathematics, MDPI, vol. 8(5), pages 1-10, May.

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