报告题目：The Numerical Solution of Random ODEs

报告时间：2017年11月11日上午8:30-11:30

报告人：Prof. Dr. P.E. Kloeden

报告摘要：Random ODEs are ordinary differential equations that include a stochastic process on their vector field. They can be analyzed pathwise using deterministic calculus. Since the sample paths of the driving stochastic process are at most Holder continuous, they lack the smoothness in their time variable to justify the convergence analysis of classical numerical scheme for ODEs. It will be briefly indicated here how new classes of numerical schemes can be derived to ensure high order of pathwise convergence depending on the nature of the driving stochastic processes. Some applications in biology will also be given.

报告题目：海洛因传播系统的建模与研究

报告时间：2017年11月11日下午14:00-17:00

报告人：李学志 教授

报告摘要：简要介绍海洛因在国内外传播概况及海洛因传播动力学研究现状，重点介绍我们在已有工作基础上建立的海洛因传播常微分方程模型、时滞模型和具有吸食年龄的海洛因传播模型，以及运用微分方程稳定性理论和构造李雅普诺夫泛函方法得到的模型平衡点的存在性、局部与全局稳定性等动力学性态。

报告题目：Asymptotic Behavior of Functional Diffusion Systems with Two-time Scales

报告时间：2017年11月12日上午8:30-11:30

报告人：华中科技大学 吴付科 教授

报告摘要：This work is concerned with functional diffusions with two-time scales in which the slow-varying component process involve path-dependent functionals and the fast-varying component process is independent of the slow-varying component. When the small parameter tends to zero, asymptotic properties are developed. The martingale method and the weak convergence areadopted to treat this problem. Since the path-dependent functionals are involved, when the martingale method and the weak convergence are used, the functional It\^{o} differential operator will be employed. By treating the fast-varying component process as random "noise", under appropriate conditions, this paper shows that the slow-varying component process involving path-dependent functionals converges weakly to a stochastic process which satisfies a stochastic functional differential equation, in which the coefficients are determined by the invariant measure of the fast-varying component.

报告题目:Uniform bounded noise induced chaotic bursting

报告时间：2017年11月12日下午14:00-17:00

报告人：华中科技大学 李骥 教授

报告摘要：Spike burst behavior is commonly observed in many nerve and endocrine cells. Periodic or chaotic burst have been of interest for a long time. Stochastic forcing is known to have non-negligible influence in many cases. We study the effect of uniformly bounded noise on the spike and burst behavior. We use the geometric method. The basic tools we use are random persistence theory, random foliation theory, random singular perturbation theory.

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