ATTEMPTING GLOBAL DYNAMICS ANALYSIS BY AUTO

摘要

Diverse fascinating phenomena surround us. The typical example would be life phenomena. We try to obtain mathematical models to understand the true nature of these phenomena through modeling processes. However, the primary question is whether we can obtain such models that represent the true nature of the phenomena. The models are not always expressed by differential equations. If we could fortunately obtain the models in the form of differential equations with appropriate modeling processes, we could try to understand the phenomena by examining the nature of the solutions. However, the mathematical models obtained would be nonlinear equations if ordinary phenomena were targeted, and computers would often be required to examine the solutions of the equations obtained. The word "nonlinear" literally means that it is not linear; this word can have a rather wide applicability. As various phenomena are collectively called nonlinear phenomena, most phenomena surrounding us are nonlinear phenomena, appearing in various forms. How should we understand these complicated phenomena? While the first step is to reproduce the phenomena by mathematical models, the final goal is to understand and elucidate the mathematical phenomena.