报告人：王玮明教授（淮阴师范学院）

报告时间：12月20日周四下午，15：00-16：00

报告地点：南校区3B-207 学术报告厅

报告题目：Bifurcation and pattern formation in a predator-prey model

摘要: In this talk, I will introduce some new results on the spatiotemporal dynamics of a Leslie-Gower predator-prey model incorporating a prey refuge subject to the Neumann boundary conditions. We mainly consider Hopf bifurcation and steady-state bifurcation which bifurcate from the constant positive steady-state of the model. In the case of Hopf bifurcation, by the center manifold theory and the normal form method, we establish the bifurcation direction and stability of bifurcating periodic solutions; in the case of steady-state bifurcation, by the local and global bifurcation theory, we prove the existence of the steady-state bifurcation, and find that there are two typical bifurcations, Turing bifurcation and Turing-Hopf bifurcation. Via numerical simulations, we find that the model exhibits not only stationary Turing pattern induced by diffusion which is dependent on space and independent of time, but also temporal periodic pattern induced by Hopf bifurcation which is dependent on time and independent of space, and spatiotemporal pattern induced by Turing-Hopf bifurcation which is dependent on both time and space. These results may enrich the pattern formation in the predator-prey model. This is a joint work with Dr. Yongli Cai.

报告人简介：王玮明，1968年6月生于甘肃正宁，理学博士。现为淮阴师范学院“翔宇学者”、数学科学学院教授；中国生物数学学会常务理事、副秘书长；淮安市传染病防控及预警重点实验室主任、淮阴师范学院生物数学研究中心主任；美国数学会《数学评论》特邀评论员。2017年入选淮安市学术技术领军人才。曾入选浙江省“新世纪151人才工程”第二层次，十二五期间任浙江省重点学科“应用数学”学科带头人。主要研究兴趣生物数学和计算机数学，主持国家自然科学基金2项，研究成果获甘肃省科技进步奖三等奖和浙江省自然科学奖三等奖各1项。