具有非局部相互作用的振荡介质中的旋转螺旋波及其规范形
Rotating spirals in oscillatory media with nonlocal interactions and their normal form
AI总结：
本文研究具有非局部耦合的振荡介质中旋转波解的存在性，通过多尺度分析与Lyapunov-Schmidt构造相结合的方法克服非局部性带来的困难，并推导出描述解领先阶行为的规范形。
摘要：
可归类为振荡介质的生物与物理系统会产生靶波和螺旋波等有趣现象。在具有局部扩散相互作用的系统中，这些结构的存在性已得到证明。本文考虑了具有非局部耦合的振荡介质的更一般情形。我们使用演化方程对这些系统进行建模，其中非局部相互作用通过扩散卷积核表示，并证明了这些系统旋转波解的存在性。由于方程的非局部性质排除了使用空间动力学的标准技术，我们采用的方法依赖于多尺度分析与类似于 Lyapunov-Schmidt 构造的结合。这一方法使我们能够推导出一个规范形（即约化方程），用以刻画这些解的领先阶行为。
英文摘要：
Biological and physical systems that can be classified as oscillatory media give rise to interesting phenomena like target patterns and spiral waves. The existence of these structures has been proven in the case of systems with local diffusive interactions. In this paper the more general case of oscillatory media with nonlocal coupling is considered. We model these systems using evolution equations where the nonlocal interactions are expressed via a diffusive convolution kernel, and prove the existence of rotating wave solutions for these systems. Since the nonlocal nature of the equations precludes the use of standard techniques from spatial dynamics, the method we use relies instead on a combination of a multiple-scales analysis and a construction similar to Lyapunov-Schmidt. This approach then allows us to derive a normal form, or reduced equation, that captures the leading order behavior of these solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
