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- W1978200099 abstract "We study the influence of internal fluctuations on phase synchronization in oscillatory reaction-diffusion systems through a master equation approach. In the limit of large system size, the probability density is analyzed by means of the eikonal approximation. This approximation yields a Hamilton-Jacobi equation for the stochastic potential, which may be reduced to coupled nonlinear diffusion equations for the phase of oscillation and (conjugate) ``momentum.'' We give explicit expressions for the coefficients of these equations in terms of averages over the deterministic periodic orbit. For one-dimensional systems, we obtain an explicit solution for the stationary stochastic potential: the width in phase, which is defined as the root mean square fluctuation in phase, characterizes the roughness of phase locking, and diverges with the system size L according to a power law $wensuremath{sim}{L}^{ensuremath{alpha}},$ with $ensuremath{alpha}=1/2.$ To study higher-dimensional systems, we show that the eikonal approximations of the diffusion-coupled oscillator problem and the Kardar-Parisi-Zhang (KPZ) equation (in the limit of small noise intensity) are equivalent. The KPZ equation governs some forms of surface growth, and the height of a growing front corresponds to the phase (the $2ensuremath{pi}$ periodicity in phase is ignored) in the diffusion-coupled oscillator problem. From the equivalence, we obtain the result that spatially synchronized states may exist only in systems with a spatial dimension greater than or equal to 3; for dimensions 1 and 2, a ``rough'' state exists in which the width (in phase) diverges algebraically with the system size, $ensuremath{alpha}>0.$" @default.
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- W1978200099 date "2000-09-01" @default.
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- W1978200099 title "Master equation approach to synchronization in diffusion-coupled nonlinear oscillators" @default.
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- W1978200099 doi "https://doi.org/10.1103/physreve.62.3303" @default.
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