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The analysis of mode-locking topology in an SIR epidemic dynamics model with impulsive vaccination control: Infinite cascade of Stern-Brocot sum trees.
- Source :
-
Chaos, Solitons & Fractals . Oct2020, Vol. 139, pN.PAG-N.PAG. 1p. - Publication Year :
- 2020
-
Abstract
- • Based on GPU parallel computing technology, the topology of mode-locking in a hybrid discrete/continuous non-smooth system is investigated. • A new cloned dynamical approach is employed to calculate the Lyapunov exponent of the hybrid system. • The mode-locking topology is organized regularly according to the elusive Stern-Brocot sum tree. • The mode-locking order is unfolded in a way that never encountered before to emerge in perfect agreement with the reciprocal of the Stern-Brocot sum tree. We report the topology of stable periodic solutions of an SIR epidemic dynamics model with impulsive vaccination control, a hybrid discrete/continuous non-smooth system, in the parameter plane spanned by the pulse period T and the quantity of pulse vaccination b. This mode-locking topology is governed by an invariant torus (a pair of frequencies) initiated from Hopf bifurcations rather than the fast-slow time scales, and its periodicity is in perfect agreement with the so-called Stern-Brocot sum tree, a derived tree from "Farey algorithm". More surprisingly, the mode-locking order is unfolded in a way that never encountered before to emerge organized according to the reciprocal of the Stern-Brocot sum tree. Furthermore, the global organization of mode-locking is not isolated structure but an infinite Stern-Brocot sum tree cascade when tuning the control parameter T. The results obtained contribute a new framework to classify mode-locking oscillations observed in the hybrid system. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09600779
- Volume :
- 139
- Database :
- Academic Search Index
- Journal :
- Chaos, Solitons & Fractals
- Publication Type :
- Periodical
- Accession number :
- 146832182
- Full Text :
- https://doi.org/10.1016/j.chaos.2020.110031