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Fractional Order Chaotic Systems

version (16.2 KB) by Ivo Petras
Numerical solutions of the fractional order chaotic systems.


Updated 26 Mar 2016

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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:

Cite As

Ivo Petras (2020). Fractional Order Chaotic Systems (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (25)

Can this function solve fractional linear differential equations??


Thanks for sharing this important results

Ana Claudia


lelf led

Really it is a nice contribution, thank you for your share!


Really it is a nice contribution, thank you for your share!

Very good submission, i am very interested by your works about fractional order systems. I have some preoccupations to plot the bifurcation diagrams in chaos systems using Fractional order.
An example could help me to solve my problem.
best regard!!!!


perfect,exactly what i needed,thank you for your selfless contribution 。

Thank you sir for your invaluable contribution.


An excellent contribution,thanks for your selfless share!

very useful to me. thanks

Very useful materials. Thank you very much.

John Mike

Thank you for your unselfish dedication!


An excellent contribution. Thank you!


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


Plug-and-play workable code. Excellent!


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

nice it is so helpful for beginner...


Description update.

Updated description. Added tag.

Description update.

Added a link to book with more details.

MATLAB Release Compatibility
Created with R14
Compatible with any release
Platform Compatibility
Windows macOS Linux