University of Groningen
Entrainment in forced Winfree systems
Zhang, Yongjiao
DOI:
10.33612/diss.143454306
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Publication date:
2020
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Zhang, Y. (2020). Entrainment in forced Winfree systems. University of Groningen.
https://doi.org/10.33612/diss.143454306
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P R O P O S I T I O N S
belonging to the thesis
E N T R A I N M E N T I N F O R C E D W I N F R E E S Y S T E M S
by
y o n g j i a o z h a n g
1. The evolution of the order parameter given by the Ott-Antonsen equations compares well to the evolution computed for the full dynamics in the non-detuned case for non-identical oscillators.
– Chapter 2
2. To compute the entrainment degree for an ensemble of oscillators in the Ott-Antonsen mean field we follow two different approaches, the direct method and the resonance tongue method, and for both approaches the results match the results in the original system.
– Chapter 2
3. The normalization method provides a very accurate approximation of the nu-merically computed resonance tongue in detuned systems.
– Chapter 3
4. The Ott-Antonsen ansatz lowers the dimension of the original system to a two-dimensional system, thus simplifying the study of the evolution of the order parameter.
– Chapter 3
5. One open question concerns the degree to which the entrainment for the obtained bimodal distribution can be obtained as a simple superposition of the entrainment for two unimodal distributions.
– Chapter 4
6. The presented methods and results can be applied to any oscillatory systems undergoing entrainment.
– Chapter 5
