Shi, Yiran2021-10-132021-10-132021-08https://hdl.handle.net/11299/224914University of Minnesota M.S. thesis. 2021. Major: Mathematics. Advisor: Richard McGehee. 1 computer file (PDF); vii 39 pages.The chaotic nature of weather systems was firstly discovered by Edward Lorenz, whowas a mathematician and meteorologist and well-known for the discovery of “Butterfly effect”. Since then, Chaos Theory triggered many interests in physics and ecology, as well as climate science. According to him, the natural system lacks periodicity, and weather cannot be predicted for a long time (Lorenz, 1963). A small inaccuracy could lead to a prediction that is the opposite of what happens in the future. For example, we cannot exactly predict the weather in Minneapolis at 10am on the 15th June 2022, whereas we can predict the average temperature of the summer based on previous data. The behavior of basic Lorenz System is highly-studied by many mathematicians and well-understood. Nevertheless, the study of averaging Lorenz system has not gone into very thoroughly.enThesis or Dissertation