报告题目：Stochastic phytoplankton allelopathy model under environmental fluctuation
报告人：原三领教授（上海理工大学）
报告时间：2016年4月28日（星期四）上午8:30
报告地点：复杂系统研究所报告厅
报告摘要：
Phytoplankton allelopathy is an ecological phenomenon that concerns the interaction among toxic-producing phytoplankton. Recently, researchers pay great attention to whether the outbreaks of the harmful algal blooms are related with the allelopathy in a random fluctuating environment. Thus, the effect of toxin-producing phytoplankton and environmental stochasticity are interesting problems in marine plankton ecology. This talk includes two parts.
In the first part, we develop and analyze a stochastic phytoplankton allelopathy model, which takes both white and colored noises into account. By using the stochastic Lyapunov functions, we investigate the positive recurrence and ergodic property of the model, which implies the existence of a stationary distribution of the solution. Moreover, we obtain the mean and variance of the stationary distribution. Our results show that both the two kinds of environmental noises and toxic substances have great impacts on the evolution of the phytoplankton populations.
In the second part, we are particularly interested in a non-autonomous toxic-producing phytoplankton allelopathy model with environmental fluctuation. For the model, we first consider the existence of the global positive solution and the boundary periodic solution. Then, by using Khasminskii’s method and Lyapunov function, we derive the sufficient conditions for the existence of the nontrivial positive stochastically periodic solution. Our results show that the allelopathic effect plays an important role in the existence of the stochastic periodic solution, for example it can lead to the decrease of the peaks of the cyclic outbreaks of the harmful algal blooms.
报告人简介：原三领，博士，上海理工大学教授，博士生导师，应用数学硕士点学科带头人，中国数学会生物数学学会常务理事，美国《Mathematical Reviews》评论员。研究方向为：微分方程与动力系统、生物数学。曾先后主持和参与完成了多项国家和省部级项目的研究工作；目前正在主持一项国家自然科学基金（面上项目）和一项上海市教委科研创新重点项目的研究工作。研究内容涉及常微分方程（泛函微分方程、随机微分方程）定性与稳定性理论、分支理论、动力系统、种群动力学、流行病动力学、海洋生态学以及生物化学工程等诸多领域，具有多学科交叉的特点。曾多次到国内和国际多所高校进行访问进修和做访问学者，已在国内外重要学术刊物上发表论文70余篇，其中SCI收录40余篇。
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