Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory

Synchronization and Control of Fractional-order or Integer-order Complex Dynamical Network

Author WangJinCheng
Tutor CaiJianPing
School Zhangzhou Normal University
Course Applied Mathematics
Keywords chaos synchronization adaptive control pinning control complex dynamicalnetwork fractional-order system combination sychronization drive-response network Lyapunov stability fractional Chen system
CLC O157.5
Type Master's thesis
Year 2012
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Synchronization and control of complex dynamical network is a hot topic in networkscience. Based on Lyapunov stability theroy and matrix theory, this thesis investigates thefollowing three problems: pinning control of fractional-order chaotic network, adaptivesynchronization of drive-response network with unknown parameters and combinationsynchronization of three fractional-order Chen systems.Firstly, based on the method of eigenvalue analysis and the stability theory offractional-order differential equations, pinning control of fractional-order chaotic network isstudied respectively in terms of diagonalization and non-diagonalization. The correspondingstable regions with different orders and different inner coupling matrix are comparedrespectively. Through the analysis of the stable regions and the distribution of the product ofeigenvalue and coupling strength, the fractional-order chaotic netwok is pinned to theequilibrium. Taking the weighted directed netwrok, non-diagonalizable netwrok and BAscale-free network as examples, simulations demonstrate the effectiveness and feasibility ofthe proposed approach. For the BA scale-free network, three pinning control strategies areconsidered: higher nodes pinned, smaller nodes pinned and random pinning. Thecorresponding number of pinning nodes is also obtained.Secondly, based on the Lyapunov stability theory and LaSalle’s invariant set theory,suitable controllers and parameter update laws are designed to achieve synchronizationbetween the drive system and response dynamical network with unknown parameters. Aweighted network and a scale-free network are used as examples to verify theoretical results.In addition, with the same network topology, synchronization time of different dynamics iscompared.Finally, we select three fractional-order Chen systems as research object and thecombination synchronization among them is achieved with suitable controllers. Based on thestability of fracional-order system and Hurwitz criterion, we give the proof and the associativecriterion. Simulation results verify the correctness of the theory and the effectiveness of the control strategy.

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