# Dynamics and bifurcation on a discontinuous differential equation

- Date:
- 14.03.16
- Times:
- 15:30
- Place:
- UAB - Dept. Matemàtiques (C1/-128)
- Speaker:
- Dongmei Xiao
- University:
- Shanghai Jiaotong University

#### Abstract:

In this talk, I will introduce a discontinuous differential equation, which describes the population model with seasonal constant-yield harvesting $h$. By mathematical analysis, we investigate the dynamics of the discontinuous differential equation, which reveals the effect of the seasonal harvesting on the survival of population. As an application, we systemically study the global dynamics of a Logstic equation with seasonal constant-yield harvesting, and prove that there exists a threshold value $h_{MSY}$ (called the maximum sustainable yield) such that the Logstic equation with seasonal constant-yield harvesting undergoes saddle-node bifurcation of periodic solution as parameter $h$ passes through $h_{MSY}$. Biologically, these theoretic results reveal that the seasonal constant-yield harvesting can increase the maximum sustainable yield such that the ecological system persists comparing to the constant-yield harvesting.