红楼Y论坛（第六十四讲）-Hopf  Cyclicity and Limit Cycle of the Two-Variable Oregonator Model for Belousov-Zhabotinsky Reaction

红楼Y论坛（第六十四讲）

Topic: Hopf  Cyclicity and Limit Cycle of the Two-Variable Oregonator Model for Belousov-Zhabotinsky Reaction

Time：15:00-16:00  Mar.29, 2023(Wednesday）

Place：Room457，Haiqin No.2

Speaker：Zecen He

Abstract：This paper is considered with a two-variable Oregonator model for Belousov-Zhabotinsky Reaction. The type and stability of the positive equilibrium, Hopf cyclicity of a weak focus, and the number of limit cycles in the first quadrant are studied. It is shown that the positive equilibrium is not a center. If the system has a positive equilibrium which is a weak focus, then it is a stable weak focus of order at most 2 and it has Hopf cyclicity 2. Moreover, after transforming the system into Li\'{e}nard equations, the conditions for nonexistence and uniqueness of limit cycle are obtained respectively in the first quadrant.