Lyapunov exponents of a class of piecewise continuous systems of\n fractional order

2014/08/25 by Marius‐F. Danca, Danca, Marius-F.
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fractional Differential Equations Solutions #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1408.5676

openalex publication_date 2014/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that a class of autonomous piecewise continuous\nsystems of fractional order has well-defined Lyapunov exponents. For this\npurpose, based on some known results from differential inclusions of integer\nand fractional order and differential equations with discontinuous right-hand\nside, the associated discontinuous initial value problem is approximated with a\ncontinuous one of fractional order. Then, the Lyapunov exponents are\nnumerically determined using, for example, the known Wolf's algorithm. Three\nexamples of piecewise continuous chaotic systems of fractional order are\nsimulated and analyzed: Sprott's system, Chen's system and Shimizu-Morioka's\nsystem.\n

Citations

• Determining Lyapunov exponents from a time series

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