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

Wang LZ, Su RQ, Huang ZG, Wang X, Wang WX, Grebogi C, Lai YC - Nat Commun (2016)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: School of Electrical, Computer and Energy Engineering, Arizona State University, 650 E. Tyler Mall, Tempe, Arizona 85287-5706, USA.

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.

No MeSH data available.


A GRN of three nodes and its attractor network.(a) Schematic illustration of a three-node GRN system. The arrowhead and bar-head edges represent activation and inhibitory regulations, respectively. The sawtooth lines specify that the corresponding edge strength is experimentally adjustable. (b) Coexisting attractors (A to H) in the phase space. (c) The underlying attractor network, where each node represents an attractor and each weighted directed link indicates that its strength can be experimentally tuned to steer the system from the starting attractor to the pointed attractor. Each grey directed link with a single arrow indicates that only one parameter is needed to achieve control, and each purple link with a double-arrow and the label 3 represent the case where three parameters are required to achieve control.
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f7: A GRN of three nodes and its attractor network.(a) Schematic illustration of a three-node GRN system. The arrowhead and bar-head edges represent activation and inhibitory regulations, respectively. The sawtooth lines specify that the corresponding edge strength is experimentally adjustable. (b) Coexisting attractors (A to H) in the phase space. (c) The underlying attractor network, where each node represents an attractor and each weighted directed link indicates that its strength can be experimentally tuned to steer the system from the starting attractor to the pointed attractor. Each grey directed link with a single arrow indicates that only one parameter is needed to achieve control, and each purple link with a double-arrow and the label 3 represent the case where three parameters are required to achieve control.

Mentions: We also study a three-node GRN system, as shown in Fig. 7a. Similar to the two-node GRN system, there exist both auto and mutual regulations among the nodes. All the interactions are assumed to be characterized by the same parameters, s and n, in the Hill function. The nonlinear dynamical equations of the system are2668:


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

Wang LZ, Su RQ, Huang ZG, Wang X, Wang WX, Grebogi C, Lai YC - Nat Commun (2016)

A GRN of three nodes and its attractor network.(a) Schematic illustration of a three-node GRN system. The arrowhead and bar-head edges represent activation and inhibitory regulations, respectively. The sawtooth lines specify that the corresponding edge strength is experimentally adjustable. (b) Coexisting attractors (A to H) in the phase space. (c) The underlying attractor network, where each node represents an attractor and each weighted directed link indicates that its strength can be experimentally tuned to steer the system from the starting attractor to the pointed attractor. Each grey directed link with a single arrow indicates that only one parameter is needed to achieve control, and each purple link with a double-arrow and the label 3 represent the case where three parameters are required to achieve control.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4834635&req=5

f7: A GRN of three nodes and its attractor network.(a) Schematic illustration of a three-node GRN system. The arrowhead and bar-head edges represent activation and inhibitory regulations, respectively. The sawtooth lines specify that the corresponding edge strength is experimentally adjustable. (b) Coexisting attractors (A to H) in the phase space. (c) The underlying attractor network, where each node represents an attractor and each weighted directed link indicates that its strength can be experimentally tuned to steer the system from the starting attractor to the pointed attractor. Each grey directed link with a single arrow indicates that only one parameter is needed to achieve control, and each purple link with a double-arrow and the label 3 represent the case where three parameters are required to achieve control.
Mentions: We also study a three-node GRN system, as shown in Fig. 7a. Similar to the two-node GRN system, there exist both auto and mutual regulations among the nodes. All the interactions are assumed to be characterized by the same parameters, s and n, in the Hill function. The nonlinear dynamical equations of the system are2668:

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: School of Electrical, Computer and Energy Engineering, Arizona State University, 650 E. Tyler Mall, Tempe, Arizona 85287-5706, USA.

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.

No MeSH data available.