1. Complex mode-locking oscillations and Stern--Brocot derivation tree in a CSTR reaction with impulsive perturbations.
- Author
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Xiao-Bo Rao, Yan-Dong Chu, Jian-Gang Zhang, and Jian-She Gao
- Subjects
- *
OSCILLATIONS , *HOPF bifurcations , *TREES , *TORUS - Abstract
A complex mode-locking (entrainment) topology underlying the continuous stirred tank reactor reaction model subjected to impulsive perturbations is identified. Employing high-resolution stability diagrams, we exhibit the global structure of mode-locking oscillations and describe how they are interconnected and how their complexity unfolds with control parameters varying. The scenarios shown in the bi-parametric planes revealed that the skeleton of Arnold's tongues is organized according to the symmetric Stern--Brocot sum tree. Moreover, the mode-locking organization is controlled by an invariant torus (a pair of frequencies) initiated from Hopf bifurcations. Interestingly, the mode-locking order is unfolded in an elusive way, that is, in perfect agreement with the reciprocal of the Stern--Brocot sum tree. The findings reported here contribute to providing a description and classification of mode-locking oscillations for the impulsive system. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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