Deterministic and Stochastic Perturbations of Dynamical Systems

动力系统的确定性和随机扰动

• 批准号: RGPIN-2015-04076
• 负责人: Yi, Yingfei
• 金额: $ 2.62万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=589580
• 关键词: Deterministic; Stochastic; Perturbations; Dynamical; Systems

Centered around perturbation theory of dynamical systems, the research program consists of three separate but related projects: I. Quasi-periodic motions in the resonance zone of a nearly integrable conservative system; II. Almost automorphic dynamics as intermittency in multi-frequency oscillatory systems; III. Stochastic stability of dissipative systems. Projects I, II concern the study of multi-frequency phenomena in nature including those arising in either conservative or dissipative biological, electrical, and mechanical systems. It is predicted by many experiments and computer simulations that systems involving multi-frequency can produce both regular and complex dynamical outcomes oscillating in multi-phases. But the mechanisms of such regularity and complexity are far from being well-understood, especially when either the multi-frequency oscillations occur in the resonance zones or systems under consideration are less integrable. Project III is a systematic study of stochastic stability from distribution perspectives at both local and global levels, for white noise perturbed finite dimensional, dissipative systems. Physical systems are often subject to noise perturbations either from their surrounding environments or from their intrinsic internal uncertainties. Analyzing the impact of noise perturbations on the dynamics of these systems then becomes a fundamental issue with respect to both modeling and analysis, but a theoretical foundation for analyzing such noise impacts from a distribution perspective needs to be further developed.

该研究项目围绕动力系统的微扰理论，由三个独立但相关的项目组成： I. 近可积保守系统共振区的准周期运动；二.多频振荡系统中的间歇性几乎自守动力学；三．耗散系统的随机稳定性。项目 I、II 涉及自然中多频率现象的研究，包括保守或耗散生物、电气和机械系统中出现的现象。许多实验和计算机模拟预测，涉及多频率的系统可以产生多相振荡的规则和复杂的动态结果。但这种规律性和复杂性的机制还远未得到充分理解，特别是当多频振荡发生在谐振区或所考虑的系统可积性较差时。项目 III 是从局部和全局层面的分布角度系统研究白噪声扰动的有限维耗散系统的随机稳定性。物理系统经常受到来自周围环境或固有内部不确定性的噪声扰动。分析噪声扰动对这些系统动力学的影响就成为建模和分析的基本问题，但从分布角度分析此类噪声影响的理论基础需要进一步发展。