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EMERGENCE OF PHASE-LOCKED STATES FOR THE WINFREE MODEL IN A LARGE COUPLING REGIMEopen access
- Authors
- Ha, Seung-Yeal; Park, Jin yeong; Ryoo, Sang Woo
- Issue Date
- Aug-2015
- Publisher
- Dept. of Mathematics, Southwest Missouri State University
- Keywords
- Emergence; Phase model; Phase-locked state; Synchronization; Winfree model
- Citation
- Discrete and Continuous Dynamical Systems, v.35, no.8, pp.3417 - 3436
- Indexed
- SCIE
SCOPUS
- Journal Title
- Discrete and Continuous Dynamical Systems
- Volume
- 35
- Number
- 8
- Start Page
- 3417
- End Page
- 3436
- ISSN
- 1078-0947
- Abstract
- We study the large-time behavior of the globally coupled Winfree model in a large coupling regime. The Winfree model is the first mathematical model for the synchronization phenomenon in an ensemble of weakly coupled limit-cycle oscillators. For the dynamic formation of phase-locked states, we provide a sufficient framework in terms of geometric conditions on the coupling functions and coupling strength. We show that in the proposed framework, the emergent phase-locked state is the unique equilibrium state and it is asymptotically stable in an l1-norm; further, we investigate its configurational structure. We also provide several numerical simulations, and compare them with our analytical results.
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Related Researcher
- Park, Jin yeong
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)