Fractional-order PWC systems without zero Lyapunov exponents |
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| Authors: | Marius-F. Danca Michal Fečkan Nikolay V. Kuznetsov Guanrong Chen |
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| Affiliation: | 1.Department of Mathematics and Computer Science,Avram Iancu University,Cluj-Napoca,Romania;2.Romanian Institute for Science and Technology,Cluj-Napoca,Romania;3.Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics,Comenius University in Bratislava, Mlynská dolina,Bratislava,Slovak Republic;4.Mathematical Institute, Slovak Academy of Sciences,Bratislava,Slovak Republic;5.Department of Applied Cybernetics,Saint-Petersburg State University,Saint Petersburg,Russia;6.Department of Mathematical Information Technology,University of Jyv?skyl?,Jyv?skyl?,Finland;7.Department of Electronic Engineering,City University of Hong Kong,Hong Kong,China |
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| Abstract: | In this paper, it is shown numerically that a class of fractional-order piece-wise continuous systems, which depend on a single real bifurcation parameter, have no zero Lyapunov exponents but can be chaotic or hyperchaotic with hidden attractors. Although not analytically proved, this conjecture is verified on several systems including a fractional-order piece-wise continuous hyperchaotic system, a piece-wise continuous chaotic Chen system, a piece-wise continuous variant of the chaotic Shimizu-Morioka system and a piece-wise continuous chaotic Sprott system. These systems are continuously approximated based on results of differential inclusions and selection theory, and numerically integrated with the Adams-Bashforth-Moulton method for fractional-order differential equations. It is believed that the obtained results are valid for many, if not most, fractional-order PWC systems. |
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