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Chaotic behavior of the CML model with respect to the state and coupling parameters

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Abstract

The main aim of this paper is the study of dynamical properties of the Laplacian-type coupled map lattice induced by the logistic family on a periodic lattice depending on two parameters: the state parameter of the logistic map and the coupling constant. For this purpose, tools like maximal Lyapunov exponent, approximate entropy, and the 0–1 test for chaos are introduced and applied to numerical simulations performed using a supercomputer.

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Acknowledgements

This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) Project “IT4Innovations excellence in science—LQ1602“; by The Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development and Innovations Project “IT4Innovations National Supercomputing Center—LM2015070“; by SGC Grant No. SP2019/125 “Qualification and quantification tools application to dynamical systems”, VŠB - Technical University of Ostrava, Czech Republic, Grant of SGS No. SP2019/84, VŠB - Technical University of Ostrava, Czech Republic.

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  1. IT4Innovations, VŠB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33, Ostrava, Czech Republic

    Marek Lampart & Tomáš Martinovič

  2. Department of Applied Mathematics, VŠB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33, Ostrava, Czech Republic

    Marek Lampart

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  1. Marek Lampart
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  2. Tomáš Martinovič
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Lampart, M., Martinovič, T. Chaotic behavior of the CML model with respect to the state and coupling parameters. J Math Chem 57, 1670–1681 (2019). https://doi.org/10.1007/s10910-019-01023-2

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