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                                                                  作者:1 来源: 日期:2018/06/28 11:16:32 人气:

                                                                  题目:Prey-predator Models with an Allee effect or Delay in Adaptive Dispersal Environment



                                                                  报告摘要:In this talk, we investigate complex dynamics of prey- predator interaction models that consider: (a) diffusion in both prey and predator; (b) an Allee effect in prey; or (c) a constant time delay. We provide rigorous mathematical results of the proposed model including: (1) the stability of non-negative constant steady states; (2) sufficient conditions that lead to Hopf/Turing bifurcations; (3) a prior estimates of positive steady states. We also perform completed analysis of the corresponding ODE model to obtain a better understanding on effects of diffusion or/and delay on the stability. Our theoretical and numerical results show that diffusion can either stabilize or destabilize the system; large delay could destabilize the system; and the combination of diffusion and delay could intensify the instability of the system. Moreover, through numerical simulations, we observe that our model, with or without Allee effect, can exhibit extremely rich pattern formations that include but not limit to strips, spotted patterns, symmetric patterns. In addition, the strength of Allee effects also plays an important role in generating distinct spatial patterns.


                                                                  饶凤 ,2012年毕业于华东师范大学获理学博士学位 。现任南京工业大学数理科学学院副教授2016.12-2018.02在美国 Arizona State University访学 。

                                                                  主要从事生物数学、微分方程及动力系统等领域的研究,主持国家自然科学基金项目青年基金和天元项目各1项、江苏省自然科学基金项目1项等 。在SCI源期刊CNSNS、DCDS-B、JMAA、JSTAT、Nonlinear Dyn.等发表20余篇。曾获“南京市第十一届自然科学优秀学术论文优秀奖”、南京工业大学“教书育人、优质服务竞赛”评为教书育人先进个人 ;指导研究生获第九届“华为杯”全国研究生数学建模竞赛一等奖 。