A geometrical approach to control and controllability of nonlinear dynamical networks

Le-Zhi Wang, Ri-Qi Su, Zi-Gang Huang, Xiao Wang, Wen-Xu Wang, Celso Grebogi, Ying-Cheng Lai

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45 Citations (Scopus)
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Abstract

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.

Original languageEnglish
Article number11323
JournalNature Communications
Volume7
DOIs
Publication statusPublished - 14 Apr 2016

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Keywords

  • q-bio.MN
  • cs.SY
  • nlin.CD
  • physics.bio-ph

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