Software Listing: Petras

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.

  • Publisher: Ivo Petras
  • Date: 10-06-2013
  • Size: 20 KB
  • Platform: Matlab, Scripts

We present a Matlab toolbox which can solve basic problems related to the Total Least Squares (TLS) method in the modeling. By illustrative examples we show how to use the TLS method for solution of: - linear regression model - nonlinear regression model - fitting data in 3D space - identification of dynamical system This toolbox requires another two functions, which are already published in Matlab Central File Exchange. Those functions will be installed to computer via supporting install package 'requireFEXpackage' included in TLS package. For more details see ReadMe.txt file. Authors: Ivo Petras, Dagmar Bednarova, Tomas Skovranek, and Igor Podlubny (Technical University of Kosice, Slovakia) Detailed description of the functions, examples and demos can be found at the link: Ivo Petras and Dagmar Bednarova: Total Least Squares...

  • Publisher: Ivo Petras
  • Date: 09-04-2013
  • Size: 10 KB
  • Platform: Matlab, Scripts

Two functions are provided for fitting data using the Mittag-Leffler function. In MLFFIT1.M, just the Mittag-Leffler function in one parameter is used. In MLFFIT2, the Mittag-Leffler function in two parameters multiplied by a power function is used. Two sample scripts are provided for the illustration of possible use. These functions require the Mittag-Leffler function (FEX submission 8738); if it is not present, a one-time download is suggested. This fitting method has been introduced and used in the following article: [1] D. Sierociuk, I.Podlubny, I.Petras, "Experimental evidence of variable-order behavior of ladders and nested ladders", http://arxiv.

  • Platform: Matlab, Scripts

A new general IIR digital fractional order differentiator/integrator based on continued fraction expansion of weighted operator which is mixed scheme of the trapezoidal (Tustin) rule and the backward difference (Euler) rule. For more details see books: [1] Ivo Petras, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, Series: Nonlinear Physical Science, 2011, ISBN 978-3-642-18100-9. http://www.springer.com/engineering/contro...8-3-642-18100-9 [2] Riccardo Caponetto, Giovanni Dongola, Luigi Fortuna and Ivo Petras, Fractional Order Systems: Modeling and Control Applications, World Scientific, Singapore, 2010, ISBN 978-9-814-30419-1.

  • Publisher: Ivo Petras
  • Date: 05-03-2013
  • Size: 10 KB
  • Platform: Matlab, Scripts

A new general FIR digital fractional order differentiator/integrator based on power series expansion of the backward difference (Euler) rule. For more details see books: [1] Ivo Petras, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, Series: Nonlinear Physical Science, 2011, ISBN 978-3-642-18100-9. http://www.springer.com/engineering/contro...8-3-642-18100-9 [2] Riccardo Caponetto, Giovanni Dongola, Luigi Fortuna and Ivo Petras, Fractional Order Systems: Modeling and Control Applications, World Scientific, Singapore, 2010, ISBN 978-9-814-30419-1. http://www.worldscibooks.

  • Publisher: Ivo Petras
  • Date: 20-03-2013
  • Size: 10 KB
  • Platform: Matlab, Scripts

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