Chaos recognition using a single nonlinear node delay-based reservoir computer

Dagobert Wenkack Liedji, Jimmi Hervé Talla Mbé and Godpromesse Kenné
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Dagobert Wenkack Liedji: University of Dschang
Jimmi Hervé Talla Mbé: University of Dschang
Godpromesse Kenné: University of Dschang

The European Physical Journal B: Condensed Matter and Complex Systems, 2022, vol. 95, issue 1, 1-9

Abstract: Abstract Chaotic dynamics are abundantly present in nature as well as in manufactured devices. While chaos in some systems is an undesired phenomenon, in others, they are advantageous because of several applications. Therefore, there is an interest in developing accurate and robust tools for detecting chaos in systems. When the equations describing the system are known, the largest Lyapunov exponent method is used to classify regular from chaotic dynamics. However, when analyzing a process, it often happens that the exact form of the underlying equations is not known. Therefore, it is important to have tools allowing chaos detection using only the time series generated by the theoretical or experimental systems. In this paper, we propose an approach using the single nonlinear node delay-based reservoir computer to separate regular from chaotic dynamics. We show that its classification capabilities are robust with an accuracy of up to 99.03%. We also study the effect of the length of the time series N on the performance of our approach and demonstrate that high accuracy is achieved with short time series ( $$N \ge 20$$ N ≥ 20 ). Moreover, we demonstrate that the reservoir computer trained with the standard map can classify the dynamical state of another system (for instance, the Lorenz system). Graphical abstract

Date: 2022
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DOI: 10.1140/epjb/s10051-022-00280-6

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