Mathematical Sciences: Lyapunov Exponents and Stable Manifolds for Stochastic Delay Systems

首席研究员将继续致力于发展具有有限记忆的随机动力系统的李雅普诺夫指数和稳定流形理论。这样的动力系统出现在许多应用科学中，作为物理现象的模型，结合了状态变量的过去历史以及随机波动或噪声的影响。一个例子是血液循环的流体动力学模型，另一个例子是人口增长的模型。确定性时滞模型的小随机扰动也很自然地导致随机微分时滞系统。这项研究将导致关于这些模型几乎肯定的动力学的发现。

The principal investigator will continue to work on developing a theory of Lyapunov exponents and stable manifolds for stochastic dynamical systems with finite memory. Such dynamical systems occur in many applied sciences as models of physical phenomena incorporating the past history of the state variables as well as the effects of random fluctuations or noise. One example would be a hydrodynamic model of blood circulation while a second would be a model for population growth. Small random perturbations of deterministic delay models also lead very naturally to stochastic differential delay systems. This research will lead to discoveries concerning the almost sure dynamics of these models.