论文标题
使用广义Lyapunov方法延续概率密度函数
Continuation of Probability Density Functions using a Generalized Lyapunov Approach
论文作者
论文摘要
数值分叉理论的技术对于研究稳定的流体流动模式与所涉及的不稳定性之间的过渡非常有用。在这里，我们提供了使用参数延续来确定固定点附近随机部分微分方程系统的概率密度函数的计算方法。关键创新是使用涉及低级别近似值的迭代方法的广义Lyapunov方程的有效解。我们在物理海洋学中使用问题应用并说明了该方法的功能，即大西洋循环的多个稳态。
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.
