Collective dynamics and control of a 3-D small-world network with time delays

Xu, Xu, Luo, Jiawei, & Gu, YuanTong (2012) Collective dynamics and control of a 3-D small-world network with time delays. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 22(11).

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The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize the 3-D network system. And with properly chosen delay and gain in the delayed feedback path, the hybrid controlled model may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or complex stranger attractor from the period-doubling bifurcation. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are analyzed. The results are further extended to any "d" dimensional network. It shows that to stabilize a "d" dimensional delayed small-world network, at least a "d – 1" order completed differential feedback is needed. This work provides a constructive suggestion for the high dimensional delayed systems.

Impact and interest:

6 citations in Scopus
3 citations in Web of Science®
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ID Code: 55797
Item Type: Journal Article
Refereed: Yes
Keywords: Time delays, small-world network, stability switches, Hopf bifurcation, chaos
DOI: 10.1142/S0218127412502811
ISSN: 0218-1274
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical and Computational Mathematics not elsewhere classified (010399)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 World Scientific Publishing Company
Deposited On: 16 Dec 2012 23:10
Last Modified: 12 Jun 2013 15:23

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