| Complexity and complex systems are the crucial research topics in the 21 st century.Complex networks,serving as the significant tools and methods to describe and understand the complex systems,summarize the complex systems as the networks consisting of a host of interacting individuals.Moreover,complex networks have been widely used in various kinds of scientific fields,such as sociology,computer sciences,and biological sciences,to name just a few.At present,it has become an important research aspect of complexity science field.Nevertheless,synchronization and control issue of complex dynamical networks,which takes the research on the nonlinear dynamics as the effective theoretical basis,is a key link of research and application of complex networks.And it has a broad application prospects in satellite navigation and positioning,secure communication,multi-agent consensus,network congestion control,and etc.The main synchronization control methods of complex dynamical networks can be divided into two kinds: one is to improve the network synchronization capability by changing the properties of the network itself,such as topology structure,coupling strength and etc;the other is to use control method which is a representative of control theory,mainly including feedback control,adaptive control,impulse control,pinning control and so on.This dissertation studies the synchronization control issue on multiple sub-networks of complex dynamical networks.Some network models are mainly studied,such as star coupling complex dynamical networks,multiple sub-networks of complex network with unknown parameters,time-controllable star-like shape complex dynamical networks,multiple linear coupled sub-networks of complex networks with pinning control,multiple nonlinearly coupled sub-networks of complex networks with non-identical nodes,and so forth.Based on the Lyapunov stability theory,control theory,stochastic differential equation theory and matrix theory,we primarily use adaptive control,feedback control and pinning control methods to study the complete synchronization,combinatorial synchronization and cluster synchronization problems of these complex dynamical networks.The main contributions and innovations of this dissertation can be summarized as follows:(1)Based on the stability theory of linear system and the nonlinear asymmetric coupling method,both the inner synchronization and the outer synchronization of star-like coupled complex networks are investigated.This synchronization scheme can not only realize the inner synchronization of the nodes within a sub-network but also the outer synchronization of the nodes between different sub-networks.Moreover,the influence of the coupling intensity factors between the nodes on the synchronization of complex networks is discussed and the corresponding stable ranges are given.Numerical simulation results are given to verify the effectiveness of the proposed scheme.(2)Based on the adaptive feedback control strategy,a combinatorial inner synchronization within a sub-network,which takes four-wing chaotic system with unknown parameters and external disturbances as node dynamics,and a combinatorial outer synchronization between different sub-networks are investigated.By introducing the star-like topological networks,only the center node within a sub-network which has direct connection to the other ones belonging to different sub-networks may need to be controlled.Hence,we only need to one controller for the individual sub-network in realizing the combinatorial inner synchronization and one controller for the combinatorial outer synchronization between different sub-networks.Furthermore,adding an auxiliary item related to the corresponding unknown parameters to the parameter update laws makes that the selection of the adaptive parameters is arbitrary.Theoretical analysis and numerical simulation indicate that the method can not only realize the combinatorial synchronization of all the nodes but also accurately identify all the unknown parameters with the given adaptive laws.In addition,the proposed scheme is testified to have good robustness to the influence of stochastic disturbances.(3)In this paper,a time-controllable combinatorial inner synchronization and outer synchronization of star-like shape networks is investigated,and then apply it to secure communication.Based on the adaptive control technique and Lyapunov stability theory,some sufficient conditions,which can ensure the realization of not only the combinatorial inner synchronization within a sub-network,but also the combinatorial outer synchronization between different sub-networks in the computable time,are obtained.Due to the fact that each sub-network can perform well alone for the combinatorial inner synchronization,and the synchronization time is computable,we can set a suitable time threshold.Once it reaches the scheduled time threshold,the control center will switch to contact with the other ones in different sub-networks for the combinatorial outer synchronization.Then,a simple secure communication scheme,which is based on the adaptive combinatorial outer synchronization between different sub-networks under the influence of stochastic noise and time-delay,is presented.Finally,numerical simulation validates that the proposed method has a good performance even under the influence of white Gaussian noise and time-delay.(4)In this paper,cluster synchronization on multiple sub-networks of complex networks with nonidentical nodes,stochastic disturbances and time-varying delays is investigated.Based on the general leader-followers' model,an improved network structure model is presented to realize the cluster synchronization on multiple sub-networks of complex networks via pinning control.Compared with the previous pinning control methods,this proposed method can extend the traditional cluster synchronization of complex networks to the cluster synchronization on multiple sub-networks of complex networks,and the introduction of the leaders' network makes the followers have much opportunities to receive information from their leaders,which provides a certain ability to resist the deliberate attacks.Based on the Lyapunov stability theory and stochastic differential equation theory,some cluster synchronization criteria and a pinning scheme are established.Theoretical analysis and numerical simulation are all given to validate that the scheme has good robustness to the stochastic disturbances or even the deliberate attacks.(5)In this paper,cluster exponential synchronization on multiple nonlinearly coupled dynamical sub-networks of complex networks with non-identical nodes and stochastic perturbations is studied.Based on the single-leader-multiple-follower's model,an improved network structure model that consists of multiple pairs of matching sub-networks is proposed.There are many leaders in each leaders' sub-network,which provides much more opportunities for these leaders to transmit information.Then,some cluster synchronization criteria are derived for both the global leaders' network and followers' network,and a suitable pinning control scheme that the nodes with very large or low degrees are good candidates for applying pinning control is given.Finally,numerical simulations are proposed to validate the feasibility and effectiveness of the proposed scheme. |
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