Theoretical models in chronotherapy: II. Periodic perturbations in a chaotic chemical reaction

Abstract

In this work, the Rössler system is used as a model for chronotherapy. We applied a periodic perturbation to the y variable to take the Rössler system from a chaotic behaviour to a simple periodic one, varying the period and amplitude of forcing. Some periodical windows and period-doubling cascades are observed. The most important of them is the large period-1 area around T ₀ = 6.154 (the period corresponding to the dominant frequency in the power spectrum). This is a wide region as is desired in a chronotherapy model, where the therapy is administered, with ample tolerance, to transform a chaotic behaviour into a periodic one.

Keywords:

• Chronotherapy
• chaotic chemical reactions
• chronobiology
• biological rhythm
• non-linear dynamics
• Rössler system

Acknowledgement

This work was supported by the agreement between Universidad del Noreste and Laboratorio SAS from Tampico, Mexico.