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Research Papers

Adaptive Synchronization of Complex Dynamical Networks in Presence of Coupling Connections With Dynamical Behavior

[+] Author and Article Information
Ali Kazemy

Department of Electrical Engineering,
Tafresh University,
Tafresh 39518-79611, Iran
e-mail: kazemy@tafreshu.ac.ir

Khoshnam Shojaei

Department of Electrical Engineering,
Najafabad Branch,
Islamic Azad University,
Najafabad 8514143131, Iran
e-mail: khoshnam.shojaee@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 14, 2018; final manuscript received March 6, 2019; published online April 8, 2019. Assoc. Editor: Bernard Brogliato.

J. Comput. Nonlinear Dynam 14(6), 061003 (Apr 08, 2019) (8 pages) Paper No: CND-18-1311; doi: 10.1115/1.4043146 History: Received July 14, 2018; Revised March 06, 2019

In this paper, the synchronization of complex dynamical networks (CDNs) is investigated, where coupling connections are expressed in terms of state-space equations. As it is shown in simulation results, such links can greatly affect the synchronization and cause synchronization loss, while many real-world networks have these types of connections. With or without time-delay, two different models of the CDNs are presented. Then, by introducing a distributed adaptive controller, the synchronization conditions are derived by utilizing the Lyapunov(–Krasovskii) theorem. These conditions are provided in the form of linear matrix inequalities (LMIs), which can be easily solved by standard LMI solvers even for large networks due to a few numbers of scalar decision variables. At the end, illustrative numerical examples are given to specify the effectiveness of the proposed methods.

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Figures

Grahic Jump Location
Fig. 1

Double-scroll attractor of the Lorenz system

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Fig. 2

The structure of considered BA scale-free network with five nodes

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Fig. 3

Dynamic model of the links

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Fig. 4

State trajectories of the network without control for α = 5 ms

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Fig. 5

Error between the network's states without control for α = 5 ms

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Fig. 6

The state trajectories of the network without control for α = 20 ms

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Fig. 7

Errors between the network's states without control for α = 20 ms

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Fig. 8

State trajectories of the network for α = 100 ms

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Fig. 9

Errors between the state of network's nodes and the isolated node

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Fig. 10

Evolution of adaptive gains ki(t) for i =1,…, 5

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Fig. 11

Trajectories of control signals applied to the network

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Fig. 12

Double-scroll attractor of the Chua's system

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Fig. 13

The structure of considered BA scale-free network with 100 nodes

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Fig. 14

State trajectories of the network with 100 nodes

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Fig. 15

Errors between the state of network's nodes and the isolated node

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Fig. 16

Evolution of adaptive gains

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Fig. 17

Trajectories of control signals applied to the network

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