Signal, Image and Video Processing

, Volume 8, Issue 1, pp 65–70 | Cite as

Chaotic dynamics of the fractional order nonlinear system with time delay

  • Vedat ÇelikEmail author
  • Yakup Demir
Original Paper


This paper presents the fractional order model of a nonlinear autonomous continuous-time difference-differential equation with only one variable. Numerical simulation results of the fractional order model demonstrate the existence of chaos when system order \(q\ge 0.2\). Values of the delay time \(\tau \) in which chaotic behavior is observed at system order \(q\) are quantitatively defined using the largest Lyapunov exponents obtained from the output time series.


Chaos Fractional operators Fractional order time delayed nonlinear system Largest Lyapunov exponents 


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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Department of Electrical Electronics Engineering, Faculty of EngineeringFirat UniversityElazigTurkey

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