Mathematica package for analysis and control of chaos in nonlinear systems
نویسندگان
چکیده
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 oneand two-dimensional maps ~the logistic and Hénon maps! and flows ~the Duffing and Rössler systems! are used throughout the article to illustrate the concepts and algorithms. © 1998 American Institute of Physics. @S0894-1866~98!01806-9#
منابع مشابه
Conservative chaotic flow generated via a pseudo-linear system
Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As an interesting nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generat...
متن کاملWebMathematica-based tools for discrete-time nonlinear control systems
The package NLControl, developed in the Institute of Cybernetics at Tallinn University of Technology within the Mathematica environment, has been made partially available over the internet using webMathematica tools. The package consists of functions that assist the solution of different modelling, analysis, and synthesis problems for nonlinear control systems, described either by state or by i...
متن کاملNonlinear Multiuser Receiver for Optimized Chaos-Based DS-CDMA Systems
Chaos based communications have drawn increasing attention over the past years. Chaotic signals are derived from non-linear dynamic systems. They are aperiodic, broadband and deterministic signals that appear random in the time domain. Because of these properties, chaotic signals have been proposed to generate spreading sequences for wide-band secure communication recently. Like conventional DS...
متن کاملBifurcation and Chaos in Size-Dependent NEMS Considering Surface Energy Effect and Intermolecular Interactions
The impetus of this study is to investigate the chaotic behavior of a size-dependent nano-beam with double-sided electrostatic actuation, incorporating surface energy effect and intermolecular interactions. The geometrically nonlinear beam model is based on Euler-Bernoulli beam assumption. The influence of the small-scale and the surface energy effect are modeled by implementing the consistent ...
متن کاملA Secure Chaos-Based Communication Scheme in Multipath Fading Channels Using Particle Filtering
In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. Unfortunately, despite the advantages of chaotic systems, Such as, noise-like correlation, easy hardware implementation, multitude of chaotic modes, flexible control of their dynamics, chaotic self-synchronization phenomena and potential communication confidence due to the very dynami...
متن کامل