论文标题
不可固化的二维边界碰撞正常形式的提要，并应用于电源转换器
A synopsis of the non-invertible, two-dimensional, border-collision normal form with applications to power converters
论文作者
论文摘要
边界碰撞正常形式是二维连续地图的规范形式，由两个仿射片组成。在本文中，我们为在不可变形的情况下提供了这个地图家族动态的指南，其中两块零件折叠在同一半平面上。我们确定出现关键分叉结构的参数制度，例如周期插入，周期添加和健壮的混乱。然后，我们将结果应用于增强转换器的经典模型，以调节直流电流的电压。众所周知，对于电路参数的一种组合，该模型表现出一个边框分叉，该分叉模仿了超临界周期倍增，并且由于转换器的开关机理而不可换。我们发现，在广泛的参数值中，即使在边境碰撞中产生的动力学通常是极度多样的，但增压转换器中的分叉只能模仿倍增的时期，尽管它可以是亚临界点。
The border-collision normal form is a canonical form for two-dimensional, continuous maps comprised of two affine pieces. In this paper we provide a guide to the dynamics of this family of maps in the non-invertible case where the two pieces fold onto the same half-plane. We identify parameter regimes for the occurrence of key bifurcation structures, such as period-incrementing, period-adding, and robust chaos. We then apply the results to a classic model of a boost converter for adjusting the voltage of direct current. It is known that for one combination of circuit parameters the model exhibits a border-collision bifurcation that mimics supercritical period-doubling and is non-invertible due to the switching mechanism of the converter. We find that over a wide range of parameter values, even though the dynamics created in border-collision bifurcations is in general extremely diverse, the bifurcation in the boost converter can only mimic period-doubling, although it can be subcritical.
