Controllability of fractional-order directed complex networks

2014 ◽  
Vol 28 (27) ◽  
pp. 1450211 ◽  
Author(s):  
Hao Zhang ◽  
Di-Yi Chen ◽  
Bei-Bei Xu ◽  
Run-Fan Zhang
Keyword(s):  
Complex Networks ◽  
Fractional Order ◽  
Mathematical Expression ◽  
Small World ◽  
Order Complex ◽  
Small World Network

This paper is a step forward to generalize the fundamentals of the conventional controllability in fractional-order complex networks. First, we discuss the existence of controllability theory of fractional-order complex networks. Furthermore, we propose stringent mathematical expression and controllable proof of fractional complex networks. Finally, three typical examples from the simplest network, the chain fractional-order network, to the Small-World network are presented to validate the correctness of the above theorem.

Robust projective outer synchronization of coupled uncertain fractional-order complex networks

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Junwei Wang ◽  
Yun Zhang
Keyword(s):  
Complex Networks ◽  
Fractional Order ◽  
Small World ◽  
Linear Matrix ◽  
Control Law ◽  
Order Complex ◽  
Outer Synchronization ◽  
World Communication ◽  
Special Cases ◽  
Communication Topology

AbstractIn this work, we propose a novel projective outer synchronization (POS) between unidirectionally coupled uncertain fractional-order complex networks through scalar transmitted signals. Based on the state observer theory, a control law is designed and some criteria are given in terms of linear matrix inequalities which guarantee global robust POS between such networks. Interestingly, in the POS regime, we show that different choices of scaling factor give rise to different outer synchrony, with various special cases including complete outer synchrony, anti-outer synchrony and even a state of amplitude death. Furthermore, it is demonstrated that although stability of POS is irrelevant to the inner-coupling strength, it will affect the convergence speed of POS. In particular, stronger inner synchronization can induce faster POS. The effectiveness of our method is revealed by numerical simulations on fractional-order complex networks with small-world communication topology.

scholarly journals Adaptive Pinning Synchronization Control of the Fractional-Order Chaos Nodes in Complex Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Darui Zhu ◽  
Ling Liu ◽  
Chongxin Liu
Keyword(s):  
Complex Network ◽  
Fractional Order ◽  
Design Methodology ◽  
Small World ◽  
Synchronization Control ◽  
Order Complex ◽  
Small World Network ◽  
Network Systems ◽  
Control Scheme ◽  
Synchronization Performance

Adaptive pinning synchronization control is studied for a class of fractional-order complex network systems which are constructed depending on small-world network algorithm. Based on the fractional-order stability theory, the suitable adaptive control scheme is designed to guarantee global asymptotic stability of all the nodes in complex network systems and the node selected algorithm is given. In numerical implementation, it is shown that the numerical solution of the fractional-order complex network systems can be obtained by applying an improved version of Adams-Bashforth-Moulton algorithm. Furthermore, simulation results are provided to confirm the validity and synchronization performance of the advocated design methodology.

Finite-time synchronization of fractional-order complex networks via hybrid feedback control

2018 ◽  
Vol 320 ◽  
pp. 69-75 ◽  
Author(s):  
Hong-Li Li ◽  
Jinde Cao ◽  
Haijun Jiang ◽  
Ahmed Alsaedi
Keyword(s):  
Feedback Control ◽  
Complex Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Order Complex

scholarly journals Sizing complex networks

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Gorka Zamora-López ◽  
Romain Brasselet
Keyword(s):  
Complex Networks ◽  
Random Graphs ◽  
Null Model ◽  
Small World ◽  
Small World Network ◽  
The Many

AbstractAmong the many features of natural and man-made complex networks the small-world phenomenon is a relevant and popular one. But, how small is a small-world network and how does it compare to others? Despite its importance, a reliable and comparable quantification of the average pathlength of networks has remained an open challenge over the years. Here, we uncover the upper (ultra-long (UL)) and the lower (ultra-short (US)) limits for the pathlength and efficiency of networks. These results allow us to frame their length under a natural reference and to provide a synoptic representation, without the need to rely on the choice for a null-model (e.g., random graphs or ring lattices). Application to empirical examples of three categories (neural, social and transportation) shows that, while most real networks display a pathlength comparable to that of random graphs, when contrasted against the boundaries, only the cortical connectomes prove to be ultra-short.

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