Global dynamics of evolution systems with spatial and temporal heterogenetics

具有时空异质性的进化系统的全局动力学

• 批准号: 227177-2009
• 负责人: Zhao, Xiaoqiang
• 金额: $ 2.04万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503787
• 关键词: Global; dynamics; evolution; systems; spatial

This research program is aimed at the global dynamics of nonlinear evolution systems with spatial and temporal heterogeneities, which are inspired by population biology and epidemiology. We will study the existence, uniqueness and global stability of steady states and periodic solutions, persistence and extinction, global converegnce and attractors, the existence, uniqueness and stability of traveling waves, and asymptotic speeds of spread (in short, spreading speeds). In this project we also propose to obtain general results on spreading speeds and monostable traveling waves for abstract evolution systems, the existence and global stability of bistable waves for monotone semiflows, and basic reproduction numbers for nonautonomous epidemic models.

该研究计划旨在研究具有时空异质性的非线性演化系统的全局动力学，其灵感来自种群生物学和流行病学。我们将研究稳态和周期解的存在性、唯一性和全局稳定性，持久性和灭绝，全局吸引子和吸引子，行波的存在性、唯一性和稳定性，以及传播的渐近速度（简称传播速度）。在这个项目中，我们还建议获得抽象发展系统的传播速度和单稳行波，单调半流的行波的存在性和全局稳定性，以及非自治传染病模型的基本再生数的一般结果。