Open Access

Determining Consecutive Periods of the Lorenz Maps

Advances in Difference Equations20102010:985982

https://doi.org/10.1155/2010/985982

Received: 18 October 2009

Accepted: 19 May 2010

Published: 16 June 2010

Abstract

Based on symbolic dynamics, the paper provides a satisfactory and necessary condition of existence for consecutive periodic orbits of the Lorenz maps. In addition, a new algorithm with computer assistance based on symbolic dynamics is proposed to find all periodic orbits up to a certain number with little computer time. Examples for consecutive periods of orbits are raised for the Lorenz maps. With a little variation, the theorems and algorithm can be applied to some other dynamic systems.

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Authors’ Affiliations

(1)
School of Mathematics and Statistics, Zhejiang University of Finance and Economics

Copyright

© FulaiWang. 2010

This article is published under license to BioMed Central Ltd. 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.