Artículos

Semiglobal Chaotification of One Class of n–Dimensional Continuous–Time Systems Via a Time–Delay Feedback

Caotificación Semiglobal de una Clase de Sistemas de n–Dimensiones de Tiempo Continuo a través Realimentación de Retardo

Konstantin Starkov and Oswaldo Cuen

Centro de Investigación y Desarrollo de Tecnología Digital (CITEDI–IPN)
Av. del Parque, 1310, Mesa de Otay, Tijuana, BC, México
konst@citedi.mx ocuen@citedi.mx
Phone:01(664)6231344 Fax: (664)6231388

Article received on December 12, 2004; accepted on November 16, 2005

Abstract

A semiglobal chaotification problem of n–dimensional polynomial continuous–time systems satisfying one special condition is examined. This problem is solved in two steps. Firstly, by using some polynomial mapping we transform the initial system to some n–th order explicit scalar ordinary differential equation with a rational nonlinearity. On the second step we apply the anticontrol feedback proposed by Wang, Chen and Yu. Our results are applied to nonlocal chaotification of three systems: the Lorenz system, the Burke–Shaw system and the Liu system.

Keywords: Polynomial systems, rational nonlinearity, chaos, anticontrol.

Resumen

En este artículo es examinado el problema de caotificación para sistemas polinomiales continuos de n–dimensiones satisfaciendo una condición especial. Este problema es resuelto en dos pasos. Primero, a través del uso de un mapeo polinomial, se transforma el sistema inicial en una ecuación diferencial ordinaria escalar de orden n con una no linealidad racional. En el segundo paso se aplica el anticontrol por retroalimentación propuesto por Wang, Chen y Yu. Los resultados de caotificación no local son aplicados a tres sistemas, el sistema de Lorenz, el sistema de Burke–Shaw y el sistema de Liu.

Palabras clave: Sistemas polinomiales, no linealidad racional, caos, anticontrol.

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