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The strength of the nanobeam chaotic vibrations is quantified through the Lyapunov exponents computed based on the Sano-Sawada, Kantz, Wolf, and Rosenstein methods. The application of a few numerical methods on each stage of the modeling procedure allowed us to achieve reliable results. In particular, we have detected chaotic and hyper-chaotic vibrations of the studied nanobeam, and our results are authentic, reliable, and accurate.We explore numerically the synchronization effects in a heterogeneous two-layer network of two-dimensiona
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