Universal Dichotomy for Dynamical Systems with Variable Delay.
Universal Dichotomy for Dynamical Systems with Variable Delay.
复制标题
可变时滞动力系统的通用二分法
DOI：
10.1103/physrevlett.118.044104
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发表时间：
2017
影响因子：
8.6
通讯作者：
G. Radons
中科院分区：
文献类型：
--
作者：
A. Otto;D. Müller;G. Radons
我们表明，与时间相关的延迟系统的动力学从根本上影响的功能形式的延迟的论点。与后者相关联的迭代映射，访问映射，和相应的Koopman算子，我们确定了两个普遍性类。第一种情况下的成员等价于具有常数时滞的系统。新的，第二类的特点是锁模行为的访问地图和渐近线性，而不是对数，缩放的李雅普诺夫谱。该隶属度以分形方式仅依赖于延迟的参数。
We show that the dynamics of systems with a time-dependent delay is fundamentally affected by the functional form of the retarded argument. Associating with the latter an iterated map, the access map, and a corresponding Koopman operator, we identify two universality classes. Members in the first are equivalent to systems with a constant delay. The new, second class is characterized by the mode-locking behavior of their access maps and by an asymptotically linear, instead of a logarithmic, scaling of the Lyapunov spectrum. The membership depends in a fractal manner only on the parameters of the delay.