Nonlinear Dynamics

, Volume 81, Issue 1–2, pp 227–237 | Cite as

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

Original Paper


In this paper, we prove that a class of piecewise continuous autonomous systems of fractional order has well-defined Lyapunov exponents. To do so, based on some known results from differential inclusions of integer order and fractional order, as well as differential equations with discontinuous right-hand sides, the corresponding discontinuous initial value problem is approximated by a continuous one with fractional order. Then, the Lyapunov exponents are numerically determined using, for example, Wolf’s algorithm. Three examples of piecewise continuous chaotic systems of fractional order are simulated and analyzed: Sprott’s system, Chen’s system, and Simizu–Morioka’s system.


Piecewise continuous function Fractional-order system  Piecewise continuous system of fractional order Lyapunov exponent Chaotic system 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceAvram Iancu UniversityCluj-NapocaRomania
  2. 2.Romanian Institute for Science and TechnologyCluj-NapocaRomania

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