异结构离散型激光时空网络的聚类同步研究
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摘要
进行了异结构离散型时空网络的聚类同步研究。首先,利用Lyapunov定理构造合适的Lyapunov函数,从而实现了离散型时空网络与目标系统的聚类同步。其次,设计了网络中变化参量的识别函数和网络同步控制器。最后,在数值模拟中,选用具有时空混沌行为的激光相位共轭波空间扩展系统、Gibbs电光时空混沌模型、Bragg声光时空混沌模型作为三个聚类的网络节点的状态方程,以单向耦合映像格子的动力学方程作为目标系统,通过仿真模拟验证其同步原理的可行性。文中设计的同步技术既适用于同结构网络的同步也适用于异结构网络的同步,因此,具有一定的普适性。
Cluster synchronization of discrete laser time-space network with different structure is researched.Firstly, the Lyapunov theorem is used to construct a suitable Lyapunov function to realize the cluster synchroniza-tion of the discrete time-space network and the target system. Secondly, the recognition function of the variation pa-rameter in network and the network synchronization controller are designed. Finally, the laser phase conjugate wavespatial expansion system with spatiotemporal chaos behavior, Gibbs electro-optical spatiotemporal chaos model andBragg acousto-optic spatiotemporal chaos model are selected as the state equations of three cluster network nodes.The dynamic equation of the coupled map lattice with single phase is used as a target system, and the feasibility ofthe synchronization scheme is verified by numerical simulation. The designed synchronization technology is suit-able to both the synchronization of the same structure networks and the synchronization of different structure net-works. Therefore, it's generally suitable.
Cluster synchronization of discrete laser time-space network with different structure is researched.Firstly, the Lyapunov theorem is used to construct a suitable Lyapunov function to realize the cluster synchroniza-tion of the discrete time-space network and the target system. Secondly, the recognition function of the variation pa-rameter in network and the network synchronization controller are designed. Finally, the laser phase conjugate wavespatial expansion system with spatiotemporal chaos behavior, Gibbs electro-optical spatiotemporal chaos model andBragg acousto-optic spatiotemporal chaos model are selected as the state equations of three cluster network nodes.The dynamic equation of the coupled map lattice with single phase is used as a target system, and the feasibility ofthe synchronization scheme is verified by numerical simulation. The designed synchronization technology is suit-able to both the synchronization of the same structure networks and the synchronization of different structure net-works. Therefore, it's generally suitable.
引文
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[29]LüL,LI Y,FAN X,et al.Outer synchronization between uncertain complex networks based on back stepping design[J].Nonlinear Dyn,2013,73(1-2):767-773.
[30]LENG H,WU Z Y.Cluster synchronization of community network with distributed time delays via impulsive control[J].Chinese Physics B,2016,15(11):159-166.
[31]FAN H,ZHAO Y,FENG J.Cluster synchronization in non-linearly coupled impulsive networks with non-identical nodes and time-varying delays[J].Let Control Theory&Applications,2016,10(7):762-771.
[32]DONG H,YE D,FENG J,et al.Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control[J].Nonlinear Dynamics,2017,87(2):727-739.
[33]WANG Y,MA Z,CAO J,et al.Adaptive cluster synchronization in directed networks with nonidentical nonlinear dynamics[J].Complexity,2016,21:380-387.
[2]PAGAN G A I,AIELLO M.The power grid as a complex network:a survey[J].Physica A,2013,392(11):2688-2700.
[3]TANG J J,WANG Y H,LIU F.Characterizing traffic time series based on complex network theory[J].Physica A,2013,392(18):4192-4201.
[4]WATTS D J,STROGATZ S H.Collective dynamics of smallworld networks[J].Nature,1998,393(6684):440-442.
[5]Barabási A L,ALBERT R.Emergence of scaling in random networks[J].Science,1999,286(5439):509-512.
[6]CAI G L,JIANG S Q,CAI S M,et al.Cluster synchronization of uncertain complex networks with desynchronizing impulse[J].Chin Phys B,2014,23(12):109-116.
[7]CAI G L,YAO Q,SHAO H J.Global synchronization of weighted cellular neural network with time-varying coupling delays[J].Commun Nonlinear Sci Numer Simul,2012,17(17):3843-3847.
[8]CAI G L,SHAO H J.Synchronization-based approach for parameters identification in delayed chaotic network[J].Chin Phys B,2010,19(6):060507.
[9]CAI S,HAO J,HE Q,et al.New results on synchronization of chaotic systems with time-varying delays via intermittent control[J].Nonlinear Dynamins,2012,67(1):393-402.
[10]YU C B,QIN J H,GAO H J.Cluster synchronization indirected networks of partial-state coupled linear systems under pinning control[J].Automatica,2014,50(9):2341-2349.
[11]MA Q,LU J W.Cluster synchronization for directed complex dynamical networks via pinning control[J].Neurocomputing,2013,101(3):354-360.
[12]ZHANG W B,TANG Y,FANG J A,et al.Exponential cluster synchronization of impulsive delayed geneticoscillators with external disturbances[J].Chaos,2011,21(4):043137.
[13]WANG Y L,CAO J D.Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems[J].Nonlinear Anal Real World Appl,2013,14(14):842-851.
[14]ZHAGN J B,MA Z J,ZHANG G.Cluster synchronization induced by one-node clusters in networks with asymmetric negative couplings[J].Chaos,2013,23(4):043128.
[15]TANG Z,FENG J W.Adaptive cluster synchronization for non delayed and delayed coupling complex networks with non identical nodes[J].Abs Appl Anal,2013,2013(2013):233-242.
[16]WU Z Y,FU X C.Cluster projective synchronization between community networks with non identical nodes[J].Phys A,2012,391(391):6190-6198.
[17]WU W,ZHOU W J,CHEN T P.Cluster synchronization of linearly coupled complex networks under pinning control[J].IEEE Trans Circuits Syst Part I:Regul.Pap,2009,56(4):829-839.
[18]CAO G L,JIANG S Q,CAI S M,et al.Cluster synchronization of overlapping uncertain complex networks with timevarying impulse disturbances[J].Nonlinear Dyn,2015,80(1):503-513.
[19]JIANG S Q,CAI G L,CAI S M,et al.Adaptive cluster general projective synchronization of complex dynamic networks in finite time[J].Commun Nonlinear Sci Numer Simulat,2015,28(1-3):194-200.
[20]SU H S,RONG Z H,CHEN M Z Q,et al.Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks[J].IEEE Trans Cybern,2010,43(1):417-420.
[21]SU H S,RONG Z H,CHEN M Z Q,et al.Pinning control or cluster synchronization of complex dynamical networks[J].IEEE Trans Cybern,2013,43(1):394-399.
[22]BAGARELLO F,FRING A.Non-self-adjoint model of a two-dimensional non commutative space with an unbounded metric[J].Phys Rev A,2013,88(4):109-112.
[23]CAI S M,ZHOU P P,LIU Z R.Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control[J].Chaos,2014,24(3):033102.
[24]LI H,NING Z,YIN Y,et al.Synchronization and state estimation for singular complex dynamical networks with time-varying delays[J].Commun Nonlinear Sci Numer Simul,2013,18(18):194-208.
[25]WANG L H,DING W,CHEN D.Synchronization schemes of a class of fuzzy cellular neural networks based on adaptive control[J].Phys Lett A,2010,374(13):1440-1449.
[26]CAI G L,YAO Q,SHAO H J.Global synchronization of weighted cellular neural network with time-varying coupling delays[J].Commun Nonlinear Sci Numer Simul,2012,17(17):3843-3847.
[26]SUN Y Z,LI W,RUAN J.Finite-time generalized outer synchronization between two different complex networks[J].Commun Theor Phys,2012,58(11):697-703.
[26]YANG Y Q,CAO J D.Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects[J].Nonlinear Anal RWA,2010,11(3):1650-1659.
[27]TAURO C B,TAMARI F A,GLEISTER P M.Synchronization in lattice-embedded scale-free networks[J].Physica A,2012,391(3):834-842.
[28]WANG S G,YAO H X,ZHENG S.A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays[J].Commun Nonlinear Sci Numer Simul,2012,17(7):2997-3004.
[29]LüL,LI Y,FAN X,et al.Outer synchronization between uncertain complex networks based on back stepping design[J].Nonlinear Dyn,2013,73(1-2):767-773.
[30]LENG H,WU Z Y.Cluster synchronization of community network with distributed time delays via impulsive control[J].Chinese Physics B,2016,15(11):159-166.
[31]FAN H,ZHAO Y,FENG J.Cluster synchronization in non-linearly coupled impulsive networks with non-identical nodes and time-varying delays[J].Let Control Theory&Applications,2016,10(7):762-771.
[32]DONG H,YE D,FENG J,et al.Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control[J].Nonlinear Dynamics,2017,87(2):727-739.
[33]WANG Y,MA Z,CAO J,et al.Adaptive cluster synchronization in directed networks with nonidentical nonlinear dynamics[J].Complexity,2016,21:380-387.