Global dynamics of some evolution equations with temporal and sptatial structure

一些具有时空结构的演化方程的全局动力学

• 批准号: RGPIN-2016-04665
• 负责人: Zou, Xingfu
• 金额: $ 2.91万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=669980
• 关键词: Global; dynamics; some; evolution; equations

This proposed research program consists of two parts: (A) investigate the dynamics of some dynamical systems arising from biology in the forms of delay differential equations and reaction-diffusion equations; (B) re-examine the predator-prey interactions by incorporating the anti-predator defence responses of the prey into the model systems. For (A), the focus will be on the impact of the temporal delay (maturation delay or latency delay) and spatial diffusion, and among the topics are the equilibria or steady states and their stability, multiplicity and spatial patterns of steady states, basins of attraction, various bifurcations, travelling wave solutions and spreading speeds. The new methodology developed and new results obtained will enhance our knowledge on the effects of temporal delays and spatial diffusion on solution behaviours and enrich the theory and methodology of dynamical systems; the results will also help us better understand the evolution processes of populations, their interactions and their spatial spreads, as well as infection and spread mechanisms of infectious diseases. All these will help us predict and control future populations of some species and some infectious diseases. For (B), some exiting well-know predator-prey models will be modified to include various anti-predator defence responses, such as reducing productions, decreasing parental care and increasing vigilance and mobility etc. The resulting new models will be analysed and compared to the existing ones. Since such responses widely exist but have been largely overlooked in existing models, such re-examinations will help us better understand predator-prey interactions and take effective measures to prevent some species from going to extinction due to direct (predation) and indirect effects (fear) from their predators.**

本研究计划由两部分组成：(A)以延迟微分方程和反应扩散方程的形式研究生物学中产生的一些动力系统的动力学；(B)通过将猎物的反捕食者防御反应纳入模型系统，重新检查捕食者-猎物的相互作用。对于(A)，重点将放在时间延迟（成熟延迟或潜伏期延迟）和空间扩散的影响上，其中包括平衡或稳态及其稳定性、稳态的多样性和空间模式、吸引力盆地、各种分岔、行波解和传播速度。所开发的新方法和获得的新结果将增强我们对时间延迟和空间扩散对解行为的影响的认识，并丰富动力系统的理论和方法；研究结果还将有助于我们更好地了解种群的进化过程、相互作用和空间传播，以及传染病的感染和传播机制。所有这些都将帮助我们预测和控制一些物种的未来种群和一些传染病。对于(B)，一些现有的众所周知的捕食者-猎物模型将被修改，以包括各种反捕食者防御反应，如减少产量，减少亲代照顾和提高警惕和机动性等。由此产生的新模型将被分析并与现有模型进行比较。由于这种反应广泛存在，但在现有的模型中很大程度上被忽视了，这样的重新检查将有助于我们更好地理解捕食者-猎物的相互作用，并采取有效措施防止一些物种由于捕食者的直接（捕食）和间接影响（恐惧）而灭绝