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Determining Consecutive Periods of the Lorenz Maps

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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Correspondence to Fulai Wang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wang, F. Determining Consecutive Periods of the Lorenz Maps. Adv Differ Equ 2010, 985982 (2010). https://doi.org/10.1155/2010/985982

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

Keywords

  • Differential Equation
  • Dynamic System
  • Partial Differential Equation
  • Computer Time
  • Ordinary Differential Equation