Observing Microscopic Transitions from Macroscopic Bursts: Instability-Mediated Resetting in the Incoherent Regime of the $D$-dimensional Generalized Kuramoto Model
| Autor: | Sarthak Chandra, Edward Ott |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Phase transition
FOS: Physical sciences General Physics and Astronomy Applied Physics (physics.app-ph) 01 natural sciences Instability 010305 fluids & plasmas Physics::Fluid Dynamics Critical point (thermodynamics) Unit vector 0103 physical sciences 010306 general physics Mathematics::Representation Theory Mathematical Physics Mathematical physics Physics Applied Mathematics Kuramoto model Quantitative Biology::Molecular Networks Statistical and Nonlinear Physics Physics - Applied Physics Critical value Nonlinear Sciences::Cellular Automata and Lattice Gases Nonlinear Sciences - Chaotic Dynamics Nonlinear Sciences - Adaptation and Self-Organizing Systems Distribution function Coupling parameter Chaotic Dynamics (nlin.CD) Adaptation and Self-Organizing Systems (nlin.AO) |
| Popis: | We consider a recently introduced $D$-dimensional generalized Kuramoto model for many $(N\gg 1)$ interacting agents in which the agent states are $D$-dimensional unit vectors. It was previously shown that, for even $D$, similar to the original Kuramoto model ($D=2$), there exists a continuous dynamical phase transition from incoherence to coherence of the time asymptotic attracting state as the coupling parameter $K$ increases through a critical value $K_c^{(+)}>0$. We consider this transition from the point of view of the stability of an incoherent state, i.e., where the $N\to\infty$ distribution function is time-independent and the macroscopic order parameter is zero. In contrast with $D=2$, for even $D>2$ there is an infinity of possible incoherent equilibria, each of which becomes unstable with increasing $K$ at a different point $K=K_c$. We show that there are incoherent equilibria for all $K_c$ within the range $(K_c^{(+)}/2)\leq K_c \leq K_c^{(+)}$. How can the possible instability of incoherent states arising at $K=K_cK_c^{(+)}$? We find, for a given incoherent equilibrium, that, if $K$ is rapidly increased from $K Comment: 15 pages, 6 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|