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Fractional Order Chaotic Systems

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Fractional Order Chaotic Systems


Ivo Petras


22 Apr 2010 (Updated )

Numerical solutions of the fractional order chaotic systems.

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This toolbox contains the functions which can be used to simulate some of the well-known fractional order chaotic systems, such as:
- Chen's system,
- Arneodo's system,
- Genesio-Tesi's system,
- Lorenz's system,
- Newton-Leipnik's system,
- Rossler's system,
- Lotka-Volterra system,
- Duffing's system,
- Van der Pol's oscillator,
- Volta's system,
- Lu's system,
- Liu's system,
- Chua's systems,
- Financial system,
- 3 cells CNN.

The functions numerically compute a solution of the fractional nonlinear differential equations, which describe the chaotic system. Each function returns the state trajectory (attractor) for total simulation time.

For more details see book:

Ivo Petras, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, Series: Nonlinear Physical Science, 2011, ISBN 978-3-642-18100-9.

or Chinese edition:

Higher Education Press, Series: Nonlinear Physical Science, 2011, ISBN 978-7-04-031534-9.

Zentralblatt MATH Database review:

MATLAB release MATLAB 7 (R14)
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Comments and Ratings (10)
03 Nov 2014 Jorge


Hi I really appreciate your toolbox. I have a question. Does the numerical technique you have used in your code has a name? I mean the way you approximate the systems with the fractional derivatives has a name?. Thanks

Comment only
08 Aug 2014 Vembarasan V

Vembarasan V

16 Apr 2014 Nguyen


20 Jan 2013 Luis Antonio Aguirre

Luis Antonio Aguirre

20 Jan 2013 Luis Antonio Aguirre

Luis Antonio Aguirre

20 Jan 2013 Luis Antonio Aguirre

Luis Antonio Aguirre

Plug-and-play workable code. Excellent!

09 Nov 2012 maha hussein

maha hussein

20 Dec 2011 ehs


17 Oct 2010 Xinsong Yang

Xinsong Yang

very good, but when adaptive controller is added to them, some problems seems arise. Will the author teach me? Thanks.

27 Apr 2010 rachana pathak

rachana pathak

nice it is so helpful for beginner...

30 Nov 2010

Added a link to book with more details.

17 Apr 2011

Description update.

29 Nov 2011

Updated description. Added tag.

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