Modified Functional Projective Synchronization of the Unidirectional and Bidirectional Hybrid Connective Star Network with Coupling Time-Delay
|
摘要
An unidirectional and bidirectional hybrid connective star network model with coupling time-delay is constructed in this paper. According to synchronization error systems, adaptive controllers for each node are structured by using the linear system stability method and the Lyapunov stability method. These adaptive controllers can realize the modified functional projective synchronization between each node of star network and an isolated node by argument and analysis. Finally, the corrective and effective of the adaptive controllers are illustrated by some numerical examples.
An unidirectional and bidirectional hybrid connective star network model with coupling time-delay is constructed in this paper. According to synchronization error systems, adaptive controllers for each node are structured by using the linear system stability method and the Lyapunov stability method. These adaptive controllers can realize the modified functional projective synchronization between each node of star network and an isolated node by argument and analysis. Finally, the corrective and effective of the adaptive controllers are illustrated by some numerical examples.
An unidirectional and bidirectional hybrid connective star network model with coupling time-delay is constructed in this paper. According to synchronization error systems, adaptive controllers for each node are structured by using the linear system stability method and the Lyapunov stability method. These adaptive controllers can realize the modified functional projective synchronization between each node of star network and an isolated node by argument and analysis. Finally, the corrective and effective of the adaptive controllers are illustrated by some numerical examples.
引文
[1]Li P,Zhang Y.Synchronization analysis of delayed complex networks with time-varying couplings[J].Physic A,2008,387:3729-3737.
[2]An X L,Zhang L,Li Y Z,et al.Synchronization analysis of complex networks with multi-weights and its application in public traffic network[J].Physic A,2014,412:149-156.
[3]Xie C R,Xu Y H,Tong D B.Synchronization of time varying delayed complex networks via impulsive control[J].Optik,2014,125(15):3781-3787.
[4]Yu R,Zhang H G,Wang Z L.Synchronization criterion of complex networks with time-delay under mixed topologies[J].Neurocomputing,2018,295:8-16.
[5]Shi L,Zhu H,Zhong S M,et al.Synchronization for time-varying complex networks based on control[J].Journal of Computational and Applied Mathematics,2016,301:178-187.
[6]Gu Y Q,Shao C,Fu X C.Complete synchronization and stability of star-shaped complex networks[J].Chaos,Solitons&Fractals,2006,28(2):480-488.
[7]Soriano-Sánchez A G,Posadas-Castillo C,Platas-Garza M A,et al.Coupling strength computation for chaotic synchronization of complex networks with multi-scroll attractors[J].Applied Mathematics and Computation,2016,275:305-316.
[8]Li S X.Linear generalized outer synchronization between two complex dynamical networks with time-varying coupling delay[J].Optik,2016,127(22):10467-10477.
[9]Wu X J,Lu H T.Projective lag synchronization of the general complex dynamical networks with distinct nodes[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(11):4417-4429.
[10]Li D K,Lian Y P,Zhang J G.Function projective synchronization of complex networks with time-varying delay coupling[J].Journal of Beijing University of Technology,2015,41(2):207-214(Ch).
[11]Nishikawa T,Motter A E.Maximum performance at minimum cost in network synchronization[J].Physic D:Nonlinear Phenomena,2006,224(1-2):77-89.
[12]Agiza H N.Chaos synchronization of Lüdynamical system[J].Nonlinear Analysis,2004,58(1/2):11-20.
[13]Wang Y W,Guan Z H.Generalized synchronization of continuous chaotic system[J].Chaos,Solitons&Fractals,2006,27(1):97-101.
[14]Li G H.Modified projective synchronization of chaotic system[J].Chaos Solitons&Fractals,2007,32(5):1786-1790.
[15]Li J F,Li N.Modified function projective synchronization of a class of chaotic systems[J].Acta Phys Sin,2011,60(8):080507-1-5(Ch).
[16]Mao B X,Cheng C R,Bu C X.Modified function projective synchronization of Lurie chaotic system[J].J of Math,2013,33(4):717-720(Ch).
[17]Wang J A,Li Z J,Liu H P.Adaptive modified function projective synchronization for four-dimensional chaotic system[J].Systems Engineering and Electronics,2010,32(8):1745-1748(Ch).
[18]Deng W,Feng J,Wu Z J,et al.Adaptive modified function projective synchronization of a class of chaotic systems with uncertainties[J].Acta Physica Sinica,2012,61(14):140503-1-8(Ch).
[19]Xue A K.Robust Optimal Control Theory and Application[M].Beijing:Science Press,2008(Ch).
[20]Wang Z,Christos V,Sifeu T K,et al.Four-wing attractors in a novel chaotic system with hyperbolic sine nonlinearity[J].Optik,2017,(131):1071-1078.
[2]An X L,Zhang L,Li Y Z,et al.Synchronization analysis of complex networks with multi-weights and its application in public traffic network[J].Physic A,2014,412:149-156.
[3]Xie C R,Xu Y H,Tong D B.Synchronization of time varying delayed complex networks via impulsive control[J].Optik,2014,125(15):3781-3787.
[4]Yu R,Zhang H G,Wang Z L.Synchronization criterion of complex networks with time-delay under mixed topologies[J].Neurocomputing,2018,295:8-16.
[5]Shi L,Zhu H,Zhong S M,et al.Synchronization for time-varying complex networks based on control[J].Journal of Computational and Applied Mathematics,2016,301:178-187.
[6]Gu Y Q,Shao C,Fu X C.Complete synchronization and stability of star-shaped complex networks[J].Chaos,Solitons&Fractals,2006,28(2):480-488.
[7]Soriano-Sánchez A G,Posadas-Castillo C,Platas-Garza M A,et al.Coupling strength computation for chaotic synchronization of complex networks with multi-scroll attractors[J].Applied Mathematics and Computation,2016,275:305-316.
[8]Li S X.Linear generalized outer synchronization between two complex dynamical networks with time-varying coupling delay[J].Optik,2016,127(22):10467-10477.
[9]Wu X J,Lu H T.Projective lag synchronization of the general complex dynamical networks with distinct nodes[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(11):4417-4429.
[10]Li D K,Lian Y P,Zhang J G.Function projective synchronization of complex networks with time-varying delay coupling[J].Journal of Beijing University of Technology,2015,41(2):207-214(Ch).
[11]Nishikawa T,Motter A E.Maximum performance at minimum cost in network synchronization[J].Physic D:Nonlinear Phenomena,2006,224(1-2):77-89.
[12]Agiza H N.Chaos synchronization of Lüdynamical system[J].Nonlinear Analysis,2004,58(1/2):11-20.
[13]Wang Y W,Guan Z H.Generalized synchronization of continuous chaotic system[J].Chaos,Solitons&Fractals,2006,27(1):97-101.
[14]Li G H.Modified projective synchronization of chaotic system[J].Chaos Solitons&Fractals,2007,32(5):1786-1790.
[15]Li J F,Li N.Modified function projective synchronization of a class of chaotic systems[J].Acta Phys Sin,2011,60(8):080507-1-5(Ch).
[16]Mao B X,Cheng C R,Bu C X.Modified function projective synchronization of Lurie chaotic system[J].J of Math,2013,33(4):717-720(Ch).
[17]Wang J A,Li Z J,Liu H P.Adaptive modified function projective synchronization for four-dimensional chaotic system[J].Systems Engineering and Electronics,2010,32(8):1745-1748(Ch).
[18]Deng W,Feng J,Wu Z J,et al.Adaptive modified function projective synchronization of a class of chaotic systems with uncertainties[J].Acta Physica Sinica,2012,61(14):140503-1-8(Ch).
[19]Xue A K.Robust Optimal Control Theory and Application[M].Beijing:Science Press,2008(Ch).
[20]Wang Z,Christos V,Sifeu T K,et al.Four-wing attractors in a novel chaotic system with hyperbolic sine nonlinearity[J].Optik,2017,(131):1071-1078.