Recovery of scalar time-delay systems from time series

被引：44

作者：

Bunner, MJ ^{[1
]}

Popp, M ^{[1
]}

Meyer, T ^{[1
]}

Kittel, A ^{[1
]}

Rau, U ^{[1
]}

Parisi, J ^{[1
]}

机构：

[1] UNIV BAYREUTH,INST PHYS,D-95440 BAYREUTH,GERMANY

来源：

PHYSICS LETTERS A | 1996年 / 211卷 / 06期

关键词：

D O I：

10.1016/0375-9601(96)00014-X

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present an analysis method that allows one to recover the differential equation of scalar time-delay systems having the form dy(t)/dt = f(y(t - tau(0))) - y(t) if only their time series are available. There exists a projection of an extremal section from the infinite-dimensional phase space to the (y(t - tau(0)),y(t))-plane, which has a fractal dimension less than or equal to one. This criterion can be used to extract the delay time tau(0) from the time series. Furthermore, the function f(Y(t - tau(0))) and, therefore, the complete time-evolution equation are obtained through a fitting procedure. The method is able to identify dynamical systems, the instability of which is time-delay induced. The method is successfully applied to experimental time series taken from two different types of electronic oscillators.

引用

页码：345 / 349

页数：5

共 9 条

[1] ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS [J].