Dynamical Study of Almost Periodic Systems with Applications

9501412易这个项目关注的是源于科学和工程问题的动力系统和微分方程的问题。它的主要目标将是研究出现在常微分方程组和抛物型微分方程中的几乎周期现象和复杂动力学。应特别注意不变环面的摄动、准周期分支、几乎周期抛物方程的动力学问题，如解的渐近行为、不变集的结构和全局吸引子的存在性等。这个项目专注于动力系统中源于科学和工程问题的问题。它的主要目标是研究流体和生物模型中出现的几乎周期性的现象和复杂的动力学。他在前作中发现的新技术将被运用到当前的研究中。***

9501412 Yi This project is focused on problems in dynamical systems and differential equations originating in science and engineering problems. Its primary goal will be to study almost periodical phenomena and complicated dynamics arising in ordinary and parabolic type of differential equations. Particular attention shall be given to problems of perturbation of invariant tori, quasi-periodic bifurcations, dynamics of almost periodical parabolic equations such as asymptotical behavior of solutions, structure of invariant sets and existence of a global attractor, etc. Techniques from topological dynamics and nonlinear analysis as well as those found by the PI in his previous works shall be employed to the current studies. %%% This project is focused on problems in dynamical systems originating in science and engineering problems. Its primary goal will be to study almost periodical phenomena and complicated dynamamics arising in fluid as well as biological models. New techniques found by the PI in his previous works shall be employed to the current studies. ***