Amplitude Equations for Locally Cubic Nonautonomous Nonlinearities
Amplitude Equations for Locally Cubic Nonautonomous Nonlinearities
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局部三次非自治非线性的振幅方程
DOI：
10.1137/s1111111103421355
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
D. Blömker
中科院分区：
文献类型：
--
作者：
D. Blömker
对于受加性噪声扰动的局部三次非线性偏微分方程系统，我们描述了小解的基本动力学。如果系统在稳定性变化点附近，则会发生时间尺度的自然分离，主模态的振幅在长时间尺度上由随机常微分方程给出。我们考虑了动态干草叉分岔的应用，低于稳定阈值的模式形成，以及在这种确定性分岔附近的随机偏微分方程的瞬态动力学。
For systems of partial differential equations (PDEs) with locally cubic nonlinearities, which are perturbed by additive noise, we describe the essential dynamics for small solutions. If the system is near a change of stability, then a natural separation of time-scales occurs and the amplitudes of the dominant modes are given on a long time-scale by a stochastic ordinary differential equation. We consider applications to dynamic pitchfork bifurcation, pattern formation below the threshold of stability, and transient dynamics of stochastic PDEs near this deterministic bifurcations.