Monitoring changes in time of chaotic nonlinear systems.

Abstract

We extend our method for classifying signals from chaotic nonlinear dynamical systems to the problem of monitoring chaotic nonlinear dynamical systems with the goal of detecting that the state of a system has changed. One potential application would be to systems where the changes are not easily detectable by spectral analysis or other linear techniques. The method is expected to be most useful in comparison to other techniques when there are other signals or noise present, some of which have a broad band frequency spectrum, and the signal of interest is associated with either a low dimensional dynamical system or a low dimensional chaotic attractor. The method is applied to data from a laboratory model of a fluidized bed reactor and to data from a gyroscope as well as to numerically generated signals from mathematical models. For the dynamical systems considered in the paper, the proposed method provides significantly better discrimination than spectral analysis. (c) 1995 American Institute of Physics.