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Journal article
Stability of Twisted States in the Continuum Kuramoto Model
SIAM journal on applied dynamical systems, v 16(1), pp 188-203
01 Jan 2017
Abstract
We study a nonlocal diffusion equation approximating the dynamics of coupled phase oscillators on large graphs. Under appropriate assumptions, the model has a family of steady state solutions called twisted states. We prove a sufficient condition for stability of twisted states with respect to perturbations in the Sobolev and BV spaces. As an application, we study the stability of twisted states in the Kuramoto model on small-world graphs.
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Details
- Title
- Stability of Twisted States in the Continuum Kuramoto Model
- Creators
- Georgi S. Medvedev - Drexel Univ, Dept Math, 3141 Chestnut St, Philadelphia, PA 19104 USAJ. Douglas Wright - Drexel Univ, Dept Math, 3141 Chestnut St, Philadelphia, PA 19104 USA
- Publication Details
- SIAM journal on applied dynamical systems, v 16(1), pp 188-203
- Publisher
- Siam Publications
- Number of pages
- 16
- Grant note
- 1412066 / Division Of Mathematical Sciences; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) DMS-1105635; DMS-1511488; DMS-1412066 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000398542800008
- Scopus ID
- 2-s2.0-85018700930
- Other Identifier
- 991019170512604721
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- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical