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Nat Commun. 2016 Apr 14;7:11323. doi: 10.1038/ncomms11323.

A geometrical approach to control and controllability of nonlinear dynamical networks.

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School of Electrical, Computer and Energy Engineering, Arizona State University, 650 E. Tyler Mall, Tempe, Arizona 85287-5706, USA.
Institute of Computational Physics and Complex Systems, Lanzhou University, 222 S. Tianshui Road, Lanzhou, Gansu 730000, China.
School of Biological and Health Systems Engineering, Arizona State University, 621 E. Tyler Mall, Tempe, Arizona 85287-9709, USA.
School of Systems Science, Beijing Normal University, 19 Xinjiekou Outer Street, Beijing, 100875, China.
Institute for Complex Systems and Mathematical Biology, King's College, Meston Walk, University of Aberdeen, Aberdeen AB24 3UE, UK.
Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Meston Walk, Aberdeen AB24 3UE, UK.
Department of Physics, Arizona State University, 550 E Tyler Drive, Tempe, Arizona 85287-1504, USA.


In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.

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