螺旋波旋转中心解析解的研究

项目名称： 螺旋波旋转中心解析解的研究

项目编号： No.11505151

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 潘军廷

作者单位： 浙江大学

项目金额： 18万元

中文摘要： 螺旋波一直是斑图动力学研究的前沿课题之一，它普遍存在于许多自然系统中，比如，从反应扩散系统中的化学波到心脏中的心电信号都可观测到螺旋波斑图结构。因此，研究螺旋波可为研究这些系统的动力学行为提供可能的理论和方法。螺旋波的旋转中心决定着螺旋波的许多动力学行为，研究螺旋波旋转中心的动力学，尤其是研究螺旋波旋转中心的解析解对螺旋波动力学的研究将具有重要意义。与目前人们关注的振荡介质以及激发期和恢复期具有相同时间尺度的强激发介质中螺旋波旋转中心的解析解不同，本项目将着重研究激发期和恢复期具有不同时间尺度的强激发介质中螺旋波旋转中心的解析解，并以此解析解为基础，进一步基于振荡介质、强激发介质（包括具有相同和不同时间尺度的激发期和恢复期）中螺旋波旋转中心的解析解，研究螺旋波拓扑荷和手征性的动力学机制。这些研究对深入认识螺旋波的动力学过程，以及对螺旋波进行人为干预和调控具有积极的意义。

中文关键词： 螺旋波；旋转中心；解析解；拓扑荷；手征性

英文摘要： Spiral wave has long been one of the frontier topics in pattern dynamics. They are universal in many natural systems. For example, we can find them from chemical waves in reaction-diffusion systems to electrocardiosignals in the heart. Thus, the studies of spiral wave may throw a light on those of the dynamics of these systems. The rotation center of spiral waves can determine many their dynamic behaviors, so studying its dynamics, especially its analytical solution plays an important role in investigating the spiral wave dynamics. The previous studies of the analytical solution for the rotation center of spiral waves mainly focused on oscillatory media and the excitable media whose time scales of the excitation and the recovery processes are the same. Different from this, this project is aimed at studying the analytical solution for the rotation center of spiral waves in the excitable media whose time scales of the excitation and the recovery processes are different. Then, based on this obtained analytical solution, we will further study the dynamics of the topological charges and the chiralities of spiral waves with the aid of the previous analytical solution for the rotation center of spiral waves in oscillatory media and the excitable media whose time scales of the excitation and the recovery processes are the same. The project will have a significance for the study of the spiral wave dynamics and for the intervene and the control of spiral waves.

英文关键词： spiral waves;rotation center;analytical solution;topological charges;chiralities