Graduation Year
2024
Document Type
Thesis
Degree
M.A.
Degree Name
Master of Arts (M.A.)
Degree Granting Department
Mathematics and Statistics
Major Professor
Razvan Teodorescu, Ph.D.
Committee Member
Sherwin Kouchekian, Ph.D.
Committee Member
Seung-Yeop Lee, Ph.D.
Keywords
Delay differential equations, Coupled oscillators, Kuromoto model
Abstract
Nature is full of synchronization phenomena, which are essential to many scientific fields like biology, chemistry, physics, and neuroscience. The Kuramoto model is a well-known theoretical model that helps explain the fundamental ideas behind synchronization dynamics [6]. Nevertheless, in practical situations, systems frequently display intrinsic latency, which can greatly impact their behavior during synchronization. This insight inspired our work, which looks at the results of adding temporal delays to the Kuramoto model. In particular, we investigate how the system’s synchronization dynamics are affected by delays. We shed light on the mechanisms underpinning synchronization in the face of temporal delays and clarify how these delays affect the system’s emergent collective behavior through research and numerical simulations.
Scholar Commons Citation
Bakhytzhan, Shaizat, "The Effect of Fixed Time Delays on the Synchronization Phase Transition" (2024). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/10165
