Journal of Applied Mathematics
Volume 2013 (2013), Article ID 590421, 14 pages
Research Article

A New Series of Three-Dimensional Chaotic Systems with Cross-Product Nonlinearities and Their Switching

1School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China
2Department of Statistics and Applied Mathematics, Hubei University of Economics, Wuhan 430205, China
3School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China

Received 31 October 2012; Accepted 25 December 2012

Academic Editor: Xinzhi Liu

Copyright © 2013 Xinquan Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper introduces a new series of three-dimensional chaotic systems with cross-product nonlinearities. Based on some conditions, we analyze the globally exponentially or globally conditional exponentially attractive set and positive invariant set of these chaotic systems. Moreover, we give some known examples to show our results, and the exponential estimation is explicitly derived. Finally, we construct some three-dimensional chaotic systems with cross-product nonlinearities and study the switching system between them.