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Title: Controlling systems that drift through a tipping point

Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory will then go to another attractor of the system. We consider the case where there are more than one of these possible final attractors, and we ask whether we can control the outcome (i.e., the attractor that ultimately captures the trajectory) using only small controlling perturbations. Specifically, we consider the problem of controlling a noisy system whose parameter slowly drifts through a saddle-node bifurcation taking place on a fractal boundary between the basins of multiple attractors. We show that, when the noise level is low, a small perturbation of size comparable to the noise amplitude applied at a single point in time can ensure that the system will evolve toward a target attracting state with high probability. For a range of noise levels, we find that the minimum size of perturbation required for control is much smaller within a time period that starts some time after the bifurcation, providing a “window of opportunity” for driving the system toward a desirable state. We refermore » to this procedure as tipping point control.« less
Authors:
 [1] ;  [2]
  1. Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208 (United States)
  2. Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742 (United States)
Publication Date:
OSTI Identifier:
22351026
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATTRACTORS; BIFURCATION; CONTROL; DISTURBANCES; FRACTALS; GREENHOUSE GASES; NOISE; PERTURBATION THEORY; PROBABILITY; TRAJECTORIES