A multi-dimensional scheme for controlling unstable periodic orbits in chaotic systems

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Abstract

The control of unstable periodic orbits (UPOs) in chaotic systems is herein investigated by applying a weighted sum of external periodic inputs. These inputs are drawn from a "generic" set of basis functions and used to stabilize different UPOs in a chaotic attractor. All parameters associated with this multi-dimensional control scheme are experimentally computed without a priori knowledge of the system, thus making it easily applicable to a wide variety of dynamical systems. The performance of this control scheme is illustrated with several well-established chaotic systems. © 2005 Elsevier B.V. All rights reserved.

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Chakravarthy, N., Tsakalis, K., Iasemidis, L. D., & Spanias, A. (2006). A multi-dimensional scheme for controlling unstable periodic orbits in chaotic systems. Physics Letters, Section A: General, Atomic and Solid State Physics, 349(1–4), 116–127. https://doi.org/10.1016/j.physleta.2005.08.087

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