报告题目: Bifurcation Analysis of a Mosquito Population Model with a Saturated Release Rate of Sterile Mosquitoes
报告人：黄继才，华中师范大学数学系
报告时间：2018年12月7日(星期五)下午5:00-6:00
报告地点：数学院4楼425报告厅
内容摘要: Release sterile mosquitoes is a method of mosquito control using area-wide inundative releases of sterile male mosquitoes to reduce reproduction in a field population of wild mosquitoes. In this talk, we consider a mosquito population model with a nonlinear saturated release rate of sterile mosquitoes and study the complex dynamics and bifurcations of the model by performing bifurcation analysis. It is shown that there are a weak focus of multiplicity 3 and a nilpotent cusp of codimension 4 for various parameter values and the model exhibits Hopf bifurcation of codimension 3 and Bogdanov-Takens bifurcation of codimension 2 as the parameter values vary. Our analysis also shows that there exists a critical release rate of sterile mosquitoes, above which the mosquitoes population can be eliminated and below which the interacting sterile and wild mosquitoes will coexist in the form of multiple periodic oscillations and steady states for some initial populations. Numerical simulations are presented to demonstrate the coexistence of a homoclinic loop and a limit cycle, the existence of two limit cycles, and the existence of three limit cycles, respectively. This is a joint work with Prof. Shigui Ruan, Prof. Pei Yu, and Yuyue Zhang.
报告人介绍：黄继才教授1999年、2002年分别本科、硕士毕业于华中师范大学数学系，2005年获得中国科学院数学与系统科学研究院数学所博士学位。现为华中师范大学教授、博士生导师。黄教授主要从事常微分方程定性理论、分支理论及其应用研究。在JDE、SIAP、DCDS-B、JMAA 等期刊发表学术论文二十多篇，先后主持国家自然科学基金4项。
