Control of noisy heteroclinic cycles

We develop a control strategy for strongly nonlinear dynamical systems possessing heteroclinic cycles connecting saddle points and subject to small random perturbations. In the absence of control, attracting cycles lead to solutions which exhibit intermittent behavior consisting of quiescent periods...

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Bibliographic Details
Published in:Physica. D 1994-04, Vol.72 (1), p.135-160
Main Authors: Coller, B.D., Holmes, Philip, Lumley, John L.
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Classical mechanics of continuous media: general mathematical aspects
Computational methods in fluid dynamics
Exact sciences and technology
Fluctuation phenomena, random processes, noise, and brownian motion
Fluid mechanics: general mathematical aspects
Nonlinear dynamics and nonlinear dynamical systems
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary:We develop a control strategy for strongly nonlinear dynamical systems possessing heteroclinic cycles connecting saddle points and subject to small random perturbations. In the absence of control, attracting cycles lead to solutions which exhibit intermittent behavior consisting of quiescent periods interrupted by rapid “bursts”. We show that suitable feedback control can retain solutions near the saddle points and hence reduce the typical bursting rate. The model studied and the form of control are motivated by our interest in reducing turbulence production in the boundary layer.
ISSN:0167-2789
1872-8022
DOI:10.1016/0167-2789(94)90172-4