论文标题
驱动的时间延迟系统中的边界碰撞
Border-collision bifurcations in a driven time-delay system
论文作者
论文摘要
我们表明，具有时间延迟和周期性强迫的简单分段线性系统产生了圆环分叉和arnold舌头的丰富分叉结构，以及参数空间的很大一部分。模型的简单性使我们能够分析研究动力学特征。具体而言，这些特征是根据相关的庞加莱地图的边境分叉来解释的。鉴于时间延迟和周期性强迫是数学模型中的常见成分，因此该分析提供了广泛适用的见解。
We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter space. The simplicity of our model enables us to study the dynamical features analytically. Specifically, these features are explained in terms of border-collision bifurcations of an associated Poincaré map. Given that time delay and periodic forcing are common ingredients in mathematical models, this analysis provides widely applicable insight.
