Homoclinic and heteroclinic orbits in a modified Lorenz system

Authors:
Zhong Li;Guanrong Chen;Wolfgang A. Halang
Affiliations:
Faculty of Electrical Engineering, Fern Universität Hagen, Hagen 58084, Germany;Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, PR China;Faculty of Electrical Engineering, Fern Universität Hagen, Hagen 58084, Germany
Venue:
Information Sciences—Informatics and Computer Science: An International Journal - Special issue: Informatics and computer science intelligent systems applications
Year:
2004

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Abstract

This paper presents a mathematically rigorous proof for the existence of chaos in a modified Lorenz system using the theory of Shil'nikov bifurcations of homoclinic and heteroclinic orbits. Together with its dynamical behaviors, which have been extensively studied, the chaotic dynamics of the modified Lorenz system are now much better understood, providing a rigorous theoretic foundation to support studies and applications of this important class of chaotic systems.