题目: Hopf bifurcations in models with chemotaxis or advection
摘要: In an evolution model, a constant equilibrium is often stable if the perturbation is also constant one, hence it is dynamically stable with respect to an ODE dynamics. More realistic models often include the effect of spatial dispersal. In classicalTuring reaction- diffusion model, an instability is caused by diffusion with different diffusion coefficients, and it generates non-constant equilibria via bifurcation. In a model with attractive and repulsive chemotaxis, and another model with advection, we show that instability of a constant equilibrium can be caused by advection or chemotaxis. In both cases, Hopf bifurcations occur so oscillatory states emerge as the result of instability. The talk is based on joint work with Ping Liu, Zhian Wang, and Jun Zhou.
史峻平，美国威廉玛丽学院(College of William and Mary) 教授。1990-93年南开大学数学基地班学习，1998年毕业于美国杨百翰大学，获博士学位。主要研究方向为偏微分方程，动力系统，分歧理论，非线性泛函分析，生物数学。现主持美国国家科学基金会基金项目1项，参加美国国家科学基金会基金项目1项，主持完成美国国家科学基金会项目1项。参加中国国家自然科学基金项目2项。获得黑龙江省科技奖2项。主持组织国际学术会议9次，在国际学术会议做大会报告/邀请报告70余次。担任两个国际知名SCI刊物编委，为60多种数学、物理、生物刊物审稿人。发表学术论文90余篇，其中被SCI收录60余篇，被SCI杂志引用700余次。在偏微分方程，分歧理论方面的研究工作受到国际上广泛重视。另外在生物数学，包括种群模型，生物化学反应，形态生成，生态系统稳定性等方面都有研究。
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