New universality in stochastic systems

随机系统的新普遍性

• 批准号: DP220100973
• 负责人: Prof Fima Klebaner
• 金额: $ 29.22万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-08-16 至 2025-08-15
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220100973
• 关键词: New; universality; stochastic; systems

This project aims to uncover new analyses and effects in the complex behaviour of non-linear systems with random noise. Many systems originate near an unstable equilibrium. This project will develop a new mathematical theory that establishes a universality in the way the long term effect of noise expresses itself as random initial conditions in the dynamics. It will fill gaps in Mathematics and make refinements to existing fundamental scientific laws by including random initial conditions as predicted by our theory. This will advance our understanding of complex systems subjected to noise and will provide significant benefits in the scientific discoveries in Biology, Ecology, Physics and other Sciences where such systems are frequently met.

该项目旨在揭示具有随机噪声的非线性系统的复杂行为的新分析和影响。许多系统起源于不稳定平衡附近。这个项目将开发一个新的数学理论，建立一个普遍性的方式，长期的影响，噪音表达自己作为随机初始条件的动态。它将填补数学的空白，并通过包括我们理论预测的随机初始条件来完善现有的基本科学定律。这将促进我们对受噪声影响的复杂系统的理解，并将为生物学、生态学、物理学和其他经常遇到此类系统的科学发现提供重大利益。