Out Lag Synchronization of Fractional Order Delayed Complex Networks with Coupling Delay via Pinning Control

This paper discusses the out lag synchronization of fractional order complex networks (FOCN) including both internal delay and coupling delay and with the employment of pinning control scheme. Using comparison theorem and constructing the auxiliary function, several synchronization criterions by linear feedback pinning control are presented. The model and the obtained results in this work are more general than the previous works. Correctness and effectiveness of the theoretical results are validated through numerical simulations.

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Cluster Projective Synchronization of Fractional-Order Complex Network via Pinning Control

Abstract and Applied Analysis ◽

10.1155/2014/314742 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6

Author(s):

Li-xin Yang ◽

Wan-sheng He ◽

Fan-di Zhang ◽

Jin-ping Jia

Keyword(s):

Differential Equation ◽

Fractional Order ◽

Stability Theory ◽

Order Differential Equation ◽

Pinning Control ◽

Projective Synchronization ◽

Order Complex ◽

Collective Phenomena ◽

Fractional Order Differential Equation ◽

Theoretical Results

Synchronization is the strongest form of collective phenomena in complex systems of interacting components. In this paper, the problem of cluster projective synchronization of complex networks with fractional-order nodes based on the fractional-order differential equation stability theory is investigated. Only the nodes in one community which have direct connections to the nodes in other communities are controlled. Some sufficient synchronization conditions are derived via pinning control. Numerical simulations are provided to show the effectiveness of the theoretical results.

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Outer Synchronization between Fractional-Order Complex Networks: A Non-Fragile Observer-based Control Scheme

Entropy ◽

10.3390/e15041357 ◽

2013 ◽

Vol 15 (12) ◽

pp. 1357-1374 ◽

Cited By ~ 8

Author(s):

Meichun Zhao ◽

Junwei Wang

Keyword(s):

Complex Networks ◽

Fractional Order ◽

Order Complex ◽

Outer Synchronization ◽

Control Scheme

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Adaptive generalized function matrix projective lag synchronization between fractional-order and integer-order complex networks with delayed coupling and different dimensions

Physica Scripta ◽

10.1088/0031-8949/88/05/055006 ◽

2013 ◽

Vol 88 (5) ◽

pp. 055006 ◽

Cited By ~ 4

Author(s):

Hao Dai ◽

Gangquan Si ◽

Lixin Jia ◽

Yanbin Zhang

Keyword(s):

Complex Networks ◽

Fractional Order ◽

Generalized Function ◽

Order Complex ◽

Lag Synchronization ◽

Integer Order ◽

Delayed Coupling ◽

Different Dimensions ◽

Projective Lag Synchronization ◽

Function Matrix

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Adaptive Synchronization of Complex Networks with Mixed Probabilistic Coupling Delays via Pinning Control

Journal of Applied Mathematics ◽

10.1155/2014/742956 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9

Author(s):

Jian-An Wang

Keyword(s):

Complex Networks ◽

Pinning Control ◽

Adaptive Synchronization ◽

Time Varying ◽

Feedback Controllers ◽

Adaptive Feedback ◽

Network Nodes ◽

Coupling Delay ◽

Low Dimensional ◽

Theoretical Results

The problem of synchronization for a class of complex networks with probabilistic time-varying coupling delay and distributed time-varying coupling delay (mixed probabilistic time-varying coupling delays) using pinning control is investigated in this paper. The coupling configuration matrices are not assumed to be symmetric or irreducible. By adding adaptive feedback controllers to a small fraction of network nodes, a low-dimensional pinning sufficient condition is obtained, which can guarantee that the network asymptotically synchronizes to a homogenous trajectory in mean square sense. Simultaneously, two simple pinning synchronization criteria are derived from the proposed condition. Numerical simulation is provided to verify the effectiveness of the theoretical results.

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