标题： 螺旋波的漂移和摆动 显示英文标题

标题： Drift and Meander of Spiral Waves

摘要： 在本论文中，我们关注反应扩散方程组的螺旋波解的动力学行为，以及它们在对称性破缺扰动下的表现。 我们提出了一种渐近理论，用于研究由于对称性破缺扰动而漂移的螺旋波的摆动（准周期性螺旋波解）。 该理论基于早期的理论：1995年Biktashev等人的刚性旋转螺旋波漂移理论，以及1996年Biktashev等人的无扰系统中螺旋波摆动理论。 我们通过首先使用1996年摆动理论的对称性商系统方法重写1995年的漂移理论，然后继续扩展该方法以研究摆动螺旋波，考虑Floquet理论并使用奇异摄动方法。 我们在简单的例子中展示了新发展的理论的工作效果。 我们还开发了商系统方法的数值实现，展示了其数值收敛性及其在标准方法难以处理的计算中的应用，并将此研究与螺旋波响应函数的计算问题联系起来。 显示英文摘要

摘要： In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion systems of equations, and how they behave when subject to symmetry breaking perturbations. We present an asymptotic theory of the study of meandering (quasiperiodic spiral wave solutions) spiral waves which are drifting due to symmetry breaking perturbations. This theory is based on earlier theories: the 1995 Biktashev et al theory of drift of rigidly rotating spirals, and the 1996 Biktashev et al theory of meander of spirals in unperturbed systems. We combine the two theories by first rewriting the 1995 drift theory using the symmetry quotient system method of the 1996 meander theory, and then go on to extend the approach to meandering spirals by considering Floquet theory and using a singular perturbation method. We demonstrate the work of the newly developed theory on simple examples. We also develop a numerical implementation of the quotient system method, demonstrate its numerical convergence and its use in calculations which would be difficult to do by the standard methods, and also link this study to the problem of calculation of response functions of spiral waves.