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arXiv · 1507.07864

Avoiding extremes using Partial Control

Suddhasattwa Das·James Yorke
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Abstract

Dynamical systems can be prone to severe fluctuations due to the presence of chaotic dynamics. This paper explains for a toy chaotic economic model how such a system can be regulated by the application of relatively weak control to keep the system confined to a bounded region of the phase space, even in the presence of strong external disturbances. Since the control here is weaker than the disturbance, the system cannot be controlled to a particular trajectory, but under certain circumstances it can be partially controlled to avoid extreme values. Partial control depends on the existence of a certain set called a "safe sets". We describe the safe set and how it varies with parameters, sometimes continuously and sometimes discontinuously.

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Suddhasattwa Das, James Yorke. 2015-07-28. Avoiding extremes using Partial Control. https://doi.org/10.1080/10236198.2015.1079181

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