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Structure Identification of Uncertain Complex Networks Based on Anticipatory Projective Synchronization.

Heng L, Xingyuan W, Guozhen T - PLoS ONE (2015)

Bottom Line: Lyapunov theorem and Barbǎlat's lemma guarantee the stability of synchronization manifold between two networks.When the synchronization is achieved, the system parameters and topology in response network can be changed to equal with the parameters and topology in drive network.A numerical example is given to show the effectiveness of the proposed method.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China.

ABSTRACT
This paper investigates a method to identify uncertain system parameters and unknown topological structure in general complex networks with or without time delay. A complex network, which has uncertain topology and unknown parameters, is designed as a drive network, and a known response complex network with an input controller is designed to identify the drive network. Under the proposed input controller, the drive network and the response network can achieve anticipatory projective synchronization when the system is steady. Lyapunov theorem and Barbǎlat's lemma guarantee the stability of synchronization manifold between two networks. When the synchronization is achieved, the system parameters and topology in response network can be changed to equal with the parameters and topology in drive network. A numerical example is given to show the effectiveness of the proposed method.

No MeSH data available.


Error system of the third node’s topology with time delay.
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pone.0139804.g014: Error system of the third node’s topology with time delay.

Mentions: If the drive and response complex networks have time delay as τ1 = 1.5, τ2 = 0.5 in Eq (16) and Eq (17), the simulation results are shown as follows. Figs 8–10 show the state of error system. Obviously, when complex networks have time delays, the system can achieve anticipatory projective synchronization under the controller Eq (9) and Eq (10). because Ei1 = Ei2 = Ei3 = 0 when t → ∞. Fig 11 shows the changing of known system parameters when the drive and response networks have time delays. The results show that when the system achieves anticipatory projective synchronization, the known parameters βi in response network can achieve unknown parameters αi even αi is changed after t > 500. Fig 12 shows the state of error system about unknown parameters Pi. The simulation results of uncertain topological identification of b3j and the state of error system about uncertain topology Q3j are shown in Fig 13 and Fig 14, respectively.


Structure Identification of Uncertain Complex Networks Based on Anticipatory Projective Synchronization.

Heng L, Xingyuan W, Guozhen T - PLoS ONE (2015)

Error system of the third node’s topology with time delay.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4596856&req=5

pone.0139804.g014: Error system of the third node’s topology with time delay.
Mentions: If the drive and response complex networks have time delay as τ1 = 1.5, τ2 = 0.5 in Eq (16) and Eq (17), the simulation results are shown as follows. Figs 8–10 show the state of error system. Obviously, when complex networks have time delays, the system can achieve anticipatory projective synchronization under the controller Eq (9) and Eq (10). because Ei1 = Ei2 = Ei3 = 0 when t → ∞. Fig 11 shows the changing of known system parameters when the drive and response networks have time delays. The results show that when the system achieves anticipatory projective synchronization, the known parameters βi in response network can achieve unknown parameters αi even αi is changed after t > 500. Fig 12 shows the state of error system about unknown parameters Pi. The simulation results of uncertain topological identification of b3j and the state of error system about uncertain topology Q3j are shown in Fig 13 and Fig 14, respectively.

Bottom Line: Lyapunov theorem and Barbǎlat's lemma guarantee the stability of synchronization manifold between two networks.When the synchronization is achieved, the system parameters and topology in response network can be changed to equal with the parameters and topology in drive network.A numerical example is given to show the effectiveness of the proposed method.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China.

ABSTRACT
This paper investigates a method to identify uncertain system parameters and unknown topological structure in general complex networks with or without time delay. A complex network, which has uncertain topology and unknown parameters, is designed as a drive network, and a known response complex network with an input controller is designed to identify the drive network. Under the proposed input controller, the drive network and the response network can achieve anticipatory projective synchronization when the system is steady. Lyapunov theorem and Barbǎlat's lemma guarantee the stability of synchronization manifold between two networks. When the synchronization is achieved, the system parameters and topology in response network can be changed to equal with the parameters and topology in drive network. A numerical example is given to show the effectiveness of the proposed method.

No MeSH data available.