Dynamical Study of Almost Periodic Systems with Applications

9501412 Yi本项目主要研究源自科学和工程问题的动力系统和微分方程问题。它的主要目标将是研究在普通和抛物型微分方程中出现的几乎周期性现象和复杂动力学。特别注意不变量环面的摄动问题、拟周期分岔问题、概周期抛物方程的动力学问题，如解的渐近行为、不变量集的结构和全局吸引子的存在性等。拓扑动力学和非线性分析的技术以及PI在他以前的工作中发现的技术将被应用到当前的研究中。这个项目主要研究源自科学和工程问题的动力系统中的问题。它的主要目标将是研究流体和生物模型中出现的几乎周期性现象和复杂动力学。PI在以前的工作中发现的新技术将被用于当前的研究。＊＊＊

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. ***