Identifying and modelling delay feedback systems

Details Identifying and modelling delay feedback systems Identifying and modelling delay feedback systems

1999-07-13

arxiv.org/abs/chao-dyn/9907019v1

Phys. Rev. Lett. 81 (1998) 558

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevLett.81.558

Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from time series data of a scalar observable, coming along with a novel method to identify and model such systems, if a single variable is fed back. Making use of special properties of the feedback structure, we can understand the structure of the system by constructing equivalent equations of motion in spaces with dimensions which can be much smaller than the dimension of the chaotic attractor. We verify our method using both numerical and experimental data.

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