论文标题
层次延迟的系统中的层流混乱
Laminar chaos in systems with quasiperiodic delay
论文作者
论文摘要
在具有定期时间变化的延迟[Phys。莱特牧师。 120，084102（2018）]。它的特征是几乎恒定的层流相，在不规则的爆发中会定期中断，其中层流相的强度水平因相位而异。在本文中，我们证明了层状混乱也可以在具有准静脉延迟的系统中观察到，我们将保守性和耗时延迟的概念推广到此类系统。事实证明，与周期性延迟观察到的周期性变化相反，层流阶段的持续时间逐渐变化，并遵循圆环图的动力学。理论和数值结果表明，将准碘延迟调制引入时间延迟系统可能会导致混乱吸引子的尺寸的巨大降低。通过改变平均延迟并保持其他参数固定，我们发现Kaplan-Yorke尺寸在几个幅度上进行了对隔离的调节，在几个尺寸上，动力学在不同类型的高维和低维类型的混沌类型之间进行了准切换。
A new type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodic time-varying delay [Phys. Rev. Lett. 120, 084102 (2018)]. It is characterized by nearly constant laminar phases, which are periodically interrupted by irregular bursts, where the intensity levels of the laminar phases vary chaotically from phase to phase. In this paper, we demonstrate that laminar chaos can also be observed in systems with quasiperiodic delay, where we generalize the concept of conservative and dissipative delays to such systems. It turns out that the durations of the laminar phases vary quasiperiodically and follow the dynamics of a torus map in contrast to the periodic variation observed for periodic delay. Theoretical and numerical results indicate that introducing a quasiperiodic delay modulation into a time-delay system can lead to a giant reduction of the dimension of the chaotic attractors. By varying the mean delay and keeping other parameters fixed, we found that the Kaplan-Yorke dimension is modulated quasiperiodically over several orders of magnitudes, where the dynamics switches quasiperiodically between different types of high- and low-dimensional types of chaos.
