论文标题
同时分叉附近的周期性轨道和放松振荡器的增强相位降低相位
Augmented Phase Reduction for Periodic Orbits Near a Homoclinic Bifurcation and for Relaxation Oscillators
论文作者
论文摘要
振荡器 - 具有稳定周期轨道的动力系统 - 在许多物理，技术和生物学兴趣的系统中都出现。标准相减少，一种基于等距的模型还原技术，可能不适合具有小降低非平凡的浮雕指数的振荡器。这需要使用增强相还原，这是一种基于等速线和等值材料的最近设计的二维还原技术。在本文中，我们计算了两个动态不同的平面系统增强相减少的分析表达式：出生于同型分叉的周期轨道和放松振荡器。为了验证我们的计算，我们在这些动态方案中模拟了模型，并将其数值计算的增强相还原与派生的分析表达式进行了比较。这些分析和数值计算有助于我们理解在标准相减少中使用增强相减少的条件可能是有利的。
Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduction technique based on isochrons, can be unsuitable for oscillators which have a small-magnitude negative nontrivial Floquet exponent. This necessitates the use of the augmented phase reduction, a recently devised two-dimensional reduction technique based on isochrons and isostables. In this article, we calculate analytical expressions for the augmented phase reduction for two dynamically different planar systems: periodic orbits born out of a homoclinic bifurcation, and relaxation oscillators. To validate our calculations, we simulate models in these dynamic regimes, and compare their numerically computed augmented phase reduction with the derived analytical expressions. These analytical and numerical calculations help us to understand conditions for which the use of augmented phase reduction over the standard phase reduction can be advantageous.
