A new version of Scilab software package for the study of dynamical systems

Abstract

This work presents a new version of a software package for the study of chaotic flows, maps and fractals [1]. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov–Sinai entropy. Various well-known examples are implemented, with the capability of the users inserting their own ODE or iterative equations. New version program summaryProgram title: Chaos v2.0Catalogue identifier: AEAP_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1275No. of bytes in distributed program, including test data, etc.: 7135Distribution format: tar.gzProgramming language: Scilab 5.1.1. Scilab 5.1.1 should be installed before running the program. Information about the installation can be found at http://wiki.scilab.org/howto/install/windows.Computer: PC-compatible running Scilab on MS Windows or LinuxOperating system: Windows XP, LinuxRAM: below 150 MegabytesClassification: 6.2Catalogue identifier of previous version: AEAP_v1_0Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 788Does the new version supersede the previous version?: YesNature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE).Solution method:1.Numerical solving of ordinary differential equations for the study of chaotic flows. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincare sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov–Sinai entropies.2.Numerical solving of iterative equations for the study of maps and fractals.Reasons for new version: The program has been updated to use the new version 5.1.1 of Scilab with new graphical capabilities [2]. Moreover, new use cases have been added which make the handling of the program easier and more efficient.Summary of revisions:1.A new use case concerning coupled predator-prey models has been added [3].2.Three new use cases concerning fractals (Sierpinsky gasket, Barnsley's Fern and Tree) have been added [3].3.The graphical user interface (GUI) of the program has been reconstructed to include the new use cases.4.The program has been updated to use Scilab 5.1.1 with the new graphical capabilities.Additional comments: The program package contains 12 subprograms.•interface.sce – the graphical user interface (GUI) that permits the choice of a routine as follows•1.sci – Lorenz dynamical system•2.sci – Chua dynamical system•3.sci – Rosler dynamical system•4.sci – Henon map•5.sci – Lyapunov exponents for Lorenz dynamical system•6.sci – Lyapunov exponent for the logistic map•7.sci – Shannon entropy for the logistic map•8.sci – Coupled predator-prey model•1f.sci – Sierpinsky gasket•2f.sci – Barnsley's Fern•3f.sci – Barnsley's TreeRunning time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE, Lyapunov exponents calculation and fractals.