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- W2801037255 abstract "By employing a semi-analytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E {bf 67}, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics of an $N$-unit ensemble described by linear and nonlinear Langevin equations with delays. In AMM, original $N$-dimensional {it stochastic} delay differential equations (SDDEs) are transformed to infinite-dimensional {it deterministic} DEs for means and correlations of local as well as global variables. Infinite-order DEs arising from the non-Markovian property of SDDE, are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), which yields $(3+m)$-dimensional deterministic DEs. Model calculations have been made for linear and nonlinear Langevin models. The stationary solution of AMM for the linear Langevin model with N=1 is nicely compared to the exact result. The synchronization induced by an applied single spike is shown to be enhanced in the nonlinear Langevin ensemble with model parameters locating at the transition between oscillating and non-oscillating states. Results calculated by AMM6 are in good agreement with those obtained by direct simulations." @default.
- W2801037255 created "2018-05-17" @default.
- W2801037255 creator A5017199677 @default.
- W2801037255 date "2003-11-03" @default.
- W2801037255 modified "2023-09-27" @default.
- W2801037255 title "Dynamics and synchronization of Langevin ensembles with time-delayed couplings" @default.
- W2801037255 hasPublicationYear "2003" @default.
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