Journal ArticleDOI
Mathematica package for analysis and control of chaos in nonlinear systems
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TLDR
A symbolic Mathematica package for analysis and control of chaos in discrete and continuous nonlinear systems is presented and some commands with which to obtain qualitative and quantitative measures of chaos are described.Abstract:
In this article a symbolic Mathematica package for analysis and control of chaos in discrete and continuous nonlinear systems is presented. We start by presenting the main properties of chaos and describing some commands with which to obtain qualitative and quantitative measures of chaos, such as the bifurcation diagram and the Lyapunov exponents, respectively. Then we analyze the problem of chaos control and suppression, illustrating the different methodologies proposed in the literature by means of two representative algorithms (linear feedback control and suppression by perturbing the system variables). A novel analytical treatment of these algorithms using the symbolic capabilities of Mathematica is also presented. Well known one- and two-dimensional maps (the logistic and Henon maps) and flows (the Duffing and Rossler systems) are used throughout the article to illustrate the concepts and algorithms. © 1998 American Institute of Physics.read more
Citations
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Proceedings ArticleDOI
Matlab Toolbox and GUI for Analyzing One-Dimensional Chaotic Maps
TL;DR: A new Matlab toolbox and GUI (graphical user interface) providing the user with a suitable toolkit for a complete analysis of discrete systems by computer and its performance by applying it to the analysis of important issues regarding one-dimensional maps.
Journal ArticleDOI
An efficient chaotic based PSO for earliness/tardiness optimization in a batch processing flow shop scheduling problem
Hadi Mokhtari,Amir Noroozi +1 more
TL;DR: Two improved discrete particle swarm optimization (PSO) algorithms are designed where most important properties of basic PSO on velocity of particles are enhanced and the experimental results demonstrate the superiority of the algorithm against others.
Journal ArticleDOI
Automatic synthesis of chaotic attractors
TL;DR: From numerical simulations, the nonlinear system can quickly be synthesized with electronic circuits and HSPICE simulations of 9-scrolls and 4 × 3-grid scrolls by using Opamps are shown in agreement with the numerical simulations.
Journal ArticleDOI
Application of the Euler and Runge–Kutta Generalized Methods for FDE and Symbolic Packages in the Analysis of Some Fractional Attractors
TL;DR: In this article, the authors apply the Euler and the fourth-order Runge-Kutta methods in the analysis of fractional order dynamical systems, namely the Lorenz, Duffing and Liu systems.
Book ChapterDOI
Numerical-Symbolic Matlab Program for the Analysis of Three-Dimensional Chaotic Systems
TL;DR: A new numerical-symbolic Matlabprogram for the analysis of three-dimensional chaotic systems is introduced that provides the users with a GUI (Graphical User Interface) that allows us to analyze any continuous three- dimensional system with a minimal input.
References
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