Configurational stability for the Kuramoto-Sakaguchi model
| Autor: | Lee DeVille, Thomas E. Carty, Jared C. Bronski |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Generalization media_common.quotation_subject General Physics and Astronomy Frustration FOS: Physical sciences 02 engineering and technology Dynamical Systems (math.DS) Pattern Formation and Solitons (nlin.PS) Fixed point Type (model theory) 01 natural sciences Stability (probability) Instability 010305 fluids & plasmas 020901 industrial engineering & automation 0103 physical sciences FOS: Mathematics Mathematics - Dynamical Systems Mathematical Physics Mathematics media_common Applied Mathematics Kuramoto model Mathematical analysis Statistical and Nonlinear Physics Nonlinear Sciences - Pattern Formation and Solitons Nonlinear Sciences - Adaptation and Self-Organizing Systems Flow (mathematics) 34D06 34D20 37G35 05C31 Adaptation and Self-Organizing Systems (nlin.AO) |
| Popis: | The Kuramoto–Sakaguchi model is a generalization of the well-known Kuramoto model that adds a phase-lag paramater or “frustration” to a network of phase-coupled oscillators. The Kuramoto model is a flow of gradient type, but adding a phase-lag breaks the gradient structure, significantly complicating the analysis of the model. We present several results determining the stability of phase-locked configurations: the first of these gives a sufficient condition for stability, and the second a sufficient condition for instability. In fact, the instability criterion gives a count, modulo 2, of the dimension of the unstable manifold to a fixed point and having an odd count is a sufficient condition for instability of the fixed point. We also present numerical results for both small ( N≤10) and large ( N=50) collections of Kuramoto–Sakaguchi oscillators. |
| Databáze: | OpenAIRE |
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