论文标题
在稳定的库拉莫托 - 西瓦辛斯基方程中的拓扑，涡度和限制周期
Topology, Vorticity and Limit Cycle in a Stabilized Kuramoto-Sivashinsky Equation
论文作者
论文摘要
通过随机分解分析了嘈杂的稳定库拉莫托 - 苏瓦辛斯基方程。为了为存在周期性固定模式的控制参数值，可以将动力学分解为具有随机电位的扩散和横向部分。固定状态在随机全球电势景观中的相对位置可以从由相互连接的低洼特征模式跨越的拓扑中获得。数值模拟证实了预测的景观。横向组件还可以预测绕固定点周围的循环类似于通用的涡流。这些驱动非线性漂移和限制基础周期性结构在某些参数空间中的循环循环运动。我们的发现可能与对深度学习神经网络等其他非线性系统的研究有关。
A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which act on a stochastic potential. The relative positions of stationary states in the stochastic global potential landscape can be obtained from the topology spanned by the low-lying eigenmodes which inter-connect them. Numerical simulations confirm the predicted landscape. The transverse component also predicts a universal class of vortex like circulations around fixed points. These drive nonlinear drifting and limit cycle motion of the underlying periodic structure in certain regions of parameter space. Our findings might be relevant in studies of other nonlinear systems such as deep learning neural networks.
