Mathematical Sciences: Stochastic Hereditary Systems

研究者计划发展一个局部稳定流形 一类非线性随机遗传系统的理论 有限的记忆 平稳附近的李雅普诺夫谱研究 将进行双曲线轨道。 预计该 构造李雅普诺夫谱将导致存在 在静止轨道周围的局部稳定流形。 在 具体的案例研究，调查人员希望获得尖锐的 最大李雅普诺夫指数的估计，并研究其依赖性 噪声方差和延迟。 提出者打算分析动力学的行为 系统依赖于机会和过去的历史， states. 建议的工作将检查这种稳定性 长期的动力系统。 该研究将得到支持 通过计算机分析特定的模型，从工程和 物理科学

The investigator plans to develop a local stable manifold theory for non-linear stochastic hereditary systems with a bounded memory. A study of the Lyapunov spectrum near stationary hyperbolic orbits will be carried out. It is expected that the construction of the Lyapunov spectrum will lead to the existence of local stable manifolds around the stationary orbits. In specific case studies, the investigator hopes to obtain sharp estimates on the top Lyapunov exponent, and study its dependence on the noise variance and the delay. The proposer intends to analyze the behavior of dynamical systems that depend on chance and on the past history of their states. The proposed work sill examine the stability of such dynamical systems in the long term. The study will be supported by computer analysis of specific models from engineering and the physical sciences.