101. A new version of Scilab software package for the study of dynamical systems
- Author
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Bordeianu, C.C., Felea, D., Beşliu, C., Jipa, Al., and Grossu, I.V.
- Subjects
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COMPUTER software , *DYNAMICS , *CHAOS theory , *FRACTALS , *NUMERICAL calculations , *NUMERICAL solutions to differential equations , *LYAPUNOV exponents - Abstract
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 summary: Program title: Chaos v2.0 Catalogue identifier: AEAP_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEAP_v2_0.html Program obtainable from: CPC Program Library, Queen''s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1275 No. of bytes in distributed program, including test data, etc.: 7135 Distribution format: tar.gz Programming 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 Linux Operating system: Windows XP, Linux RAM: below 150 Megabytes Classification: 6.2 Catalogue identifier of previous version: AEAP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 788 Does the new version supersede the previous version?: Yes Nature 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 Tree Running 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. References: [[1]] C.C. Bordeianu, C. Besliu, Al. Jipa, D. Felea, I. V. Grossu, Comput. Phys. Comm. 178 (2008) 788. [[2]] S. Campbell, J.P. Chancelier, R. Nikoukhah, Modeling and Simulation in Scilab/Scicos, Springer, 2006. [[3]] R.H. Landau, M.J. Paez, C.C. Bordeianu, A Survey of Computational Physics, Introductory Computational Science, Princeton University Press, 2008. [Copyright &y& Elsevier]
- Published
- 2009
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