This thesis considers the phenomenon which a simple switch dynamical system. A switch dynamical system is a system which cuts and changes two or more dynamical systems with a switch. It is known that this system will present various phenomena, such as chaos, torus and a stable periodical phenomenon. Moreover, also in engineering, it is important for it to be related to an inverter circuit, a sleep awakening phenomenon, etc., and to analyze such stability. First, a switch dynamical system only with a periodic threshold is analyzed. Here, operation of a system is analyzed using a one-dimensional phase map. Moreover, it is shown clearly in which parameter domain phenomena which a system presents, such as a stable cycle and Taurus, happen. Next, the system which added the compulsive switch to the periodic threshold is considered. A compulsive switch refers to changing inclination negatively compulsorily in the same phase. A state variable can define a one-dimensional phase map by adding this switching rule. Thereby, the periodic point exploring method for considering in the following chapter is smoothly applicable. Moreover, more variegated phenomena, such as chaos, are presented by adding a switching rule. Finally, exploring and stabilization process based on bisection method.

114 工学部 (旧) ・工学研究科 ＞ 学位論文 ＞ 修士論文