Systematic Review of Geometrical Approaches and Analytical Integration for Chen’s System

Ene, Remus-Daniel; Pop, Camelia A.; Petrişor, Camelia

doi:10.3390/math8091530

Cited by 1 publication

(1 citation statement)

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“…Five known chaotic systems of integer orders were considered in this study: Lorenz, Chua, Rossler, Chen, and Lu [22]- [25]. We also include the two fractional-order (FO) systems: FO Rossler and FO Chen [26]- [28].…”

Section: A Case Studies 1) Known Chaotic Attractorsmentioning

confidence: 99%

Detection of Chaos Using Reservoir Computing Approach

et al. 2022

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Detection of chaos in time series is of utmost importance in many scientific fields. Indeed, the presence of chaos and its significance, especially in multidimensional systems, plays an essential role in the control and analysis of such systems, and in their practical use in a variety of applications. In this paper, we demonstrate a new methodology for the detection of chaos in time series using a reservoir computing (RC) paradigm called conceptor-driven network (ConDN). Case studies on the known chaotic attractors (i.e. Lorenz, Rossler, Chua) of integer (conventional) and non-integer (fractional-order) orders, as well as a physically simulated and designed spintronic device (NCVO) are used in this study to validate the proposed chaos detection approach. The proposed chaos detection approach is tested on clean and noisy time series of the mentioned attractors. It outperforms the 0-1 chaos detection test and the largest Lyapunov exponent (LLE) estimation approach especially in the high noise-level conditions. In addition, the proposed approach is capable of differentiating the time series generated by the systems whose dynamics is at the edge of chaos. The simplicity of use of the proposed chaos detection approach can be counted, as well, as one of its main advantages over traditional chaos detection methods.INDEX TERMS chaos detection, time series, reservoir computing, conceptors;

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Section: A Case Studies 1) Known Chaotic Attractorsmentioning

confidence: 99%