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Article overview
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Exactly solvable phase oscillator models with synchronization dynamics | L. L. Bonilla
; C. Perez-Vicente
; F. Ritort
; J. Soler
; | Date: |
4 Mar 1998 | Subject: | Statistical Mechanics; Disordered Systems and Neural Networks | cond-mat.stat-mech cond-mat.dis-nn | Abstract: | Populations of phase oscillators interacting globally through a general coupling function $f(x)$ have been considered. In the absence of precessing frequencies and for odd-coupling functions there exists a Lyapunov functional and the probability density evolves toward stable stationary states described by an equilibrium measure. We have then proposed a family of exactly solvable models with singular couplings which synchronize more easily as the coupling becomes less singular. The stationary solutions of the least singular coupling considered, $f(x)=$ sign$(x)$, have been found analytically in terms of elliptic functions. This last case is one of the few non trivial models for synchronization dynamics which can be analytically solved. | Source: | arXiv, cond-mat/9803055 | Services: | Forum | Review | PDF | Favorites |
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