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Theory and Modern Applications

Determining Consecutive Periods of the Lorenz Maps


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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Wang, F. Determining Consecutive Periods of the Lorenz Maps. Adv Differ Equ 2010, 985982 (2010).

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