论文标题
非线性驱动振荡器的周期轨道的生长和性能
Growth and performance of the periodic orbits of a nonlinear driven oscillator
论文作者
论文摘要
周期性的轨道是了解非线性系统动力学的基础。在这项工作中，我们关注有关周期性轨道感兴趣的两个方面，在耗散映射的背景下，这些图是从具有快速放松和极限周期的非线性驱动振荡器的原型模型中得出的。对于此地图，我们通过使用与给定的周期性轨道相关的过渡矩阵，从数值上显示了在参数空间的某些区域中周期性轨道数量的指数增长，并为这种增长率提供了分析。此外，我们提供数值证据，以支持最佳轨道（最大化时间平均的轨道）通常是不稳定的周期性轨道，而较低的轨道则通过数值比较其在正弦曲线函数的家族中的性能。
Periodic orbits are fundamental to understand the dynamics of nonlinear systems. In this work, we focus on two aspects of interest regarding periodic orbits, in the context of a dissipative mapping, derived from a prototype model of a non-linear driven oscillator with fast relaxation and a limit cycle. For this map, we show numerically the exponential growth of periodic orbits quantity in certain regions of the parameter space and provide an analytical bound for such growth rate, by making use of the transition matrix associated with a given periodic orbit. Furthermore, we give numerical evidence to support that optimal orbits, those that maximize time averages, are often unstable periodic orbits with low period, by numerically comparing their performance under a family of sinusoidal functions.
