威尼斯人

邀请报告摘要

基于动力学的组合药物研究

王瑞琦  上海大学 rqwang@shu.edu.cn

该报告主要从非线性动力学的角度讨论如何研究组合药物，包括药物靶点的筛选以及组合药物的协作型的判定等。该研究为组合药物的研究提供了新方法与思路。

Spatiotemporal dynamics of the diffusive mussel-algae model

宋永利  杭州师范大学  syl.mail@163.com

Intertidal mussels can self-organize into periodic spot, stripe, labyrinth and gap patterns range from centimeters to meters scales. The leading mathematical explanations for these phenomena are the reaction-diffusion-advection model and phase separation model. This paper is continued in the series studies on analytical understanding of the existence of pattern solutions in the reaction-diffusion mussel-algae model. The stability of the positive constant steady state, the existence of Hopf and steady state bifurcations are studied by analyzing the corresponding characteristic equation. Furthermore, we focus on the Turing-Hopf (TH) bifurcation and obtain the explicit dynamical classification in its neighborhood by calculating and investigating the normal form on the center manifold. Using theoretical and numerical simulations, we demonstrates that this TH interaction would significantly enhance the diversity of spatial patterns and trigger the alternative paths for the patterns development.

Threshold dynamics of a partially degenerate viral infection model with spatial heterogeneity

舒洪英  陕西师范大学  hshu@tongji.edu.cn

In this talk, we study a general viral infection model with spatial diffusion in virus and two types of infection mechanisms. The model is a partially degenerate reaction-diffusion system, whose solution map is not compact. We identify the basic reproduction number R0 and explore the properties of R0 when the virus diffusion parameter varies from zero to infinity. Moreover, we demonstrate that the basic reproduction number is a threshold parameter for the global dynamics of our model system Numerical simulation supports our theoretical results and suggests an interesting phenomenon: boundary layer and internal layer may occur when the diffusion parameter tends to zero.

复杂网络系统的有限时间与固定时间控制

蔡水明  江苏大学  caishuiming2008@126.com

在复杂网络系统群体行为的控制研究中，如何缩短收敛时间是一个重要的问题。对于一个实际的复杂网络系统，往往希望通过尽可能低的控制成本、尽可能快地在有限时间或固定时间内实现网络的群体行为。解决这个问题的一种有效方法是利用有限时间或固定时间控制技术来优化收敛时间，使得网络系统能在有限时间或固定时间内实现群体行为。近年来，研究人员已经开始探讨非线性系统及复杂网络系统的有限时间或固定时间稳定性、一致和同步等问题，并取得了一些重要的结果。本报告介绍一些复杂网络系统的有限时间和固定时间控制的研究结果及其相关进展。