Determining Consecutive Periods of the Lorenz Maps. (16th June 2010)

• Record Type: Journal Article
• Authors: Wang, Fulai
• Other Names: Melnik Roderick Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2010(2010)
• Publication Date: 2010-06-16
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2010/985982
• Languages: English
• ISSNs: 1687-1847

Abstract

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.