Complex mode-locking oscillations and Stern–Brocot derivation tree in a CSTR reaction with impulsive perturbations

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 interco...

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Veröffentlicht in:Chaos (Woodbury, N.Y.) N.Y.), 2020-11, Vol.30 (11), p.113117-113117
Hauptverfasser: Rao, Xiao-Bo, Chu, Yan-Dong, Zhang, Jian-Gang, Gao, Jian-She
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Sprache:eng
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Zusammenfassung: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.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0017737