Pinning synchronization of two general complex networks with periodically intermittent control
<jats:title>Abstract</jats:title> <jats:p> In this paper, the method of periodically pinning intermittent control is introduced to solve the problem of outer synchronization between two complex networks. Based on the Lyapunov stability theory, differential inequality method and adaptive technique, some simple synchronous criteria have been derived analytically. At last, both the theoretical and numerical analysis illustrate the effectiveness of the proposed control methodology. This method not only reduces the conservatism of control gain but also saves the cost of production.These advantages make this method having a large application scope in the real production process.</jats:p>
Wang (2002), Pinning a complex dynamical network to its equilibrium Circurts and Systems, IEEE Trans, 49, 54. ; Zhou (2013), Synchronization in complex dynamical networks with interval time - varying coupling delays, Nonlinear Dynamics, 72. ; Boyed (null), Linear Matrix Inequalities in System and Control Theory for Industrial and Applied Mathematics, Society SIAM, 1994. ; Wang (2002), Complex networks : topology , dynamics and synchronization of Bifurcation and, Chaos, 12, 885. ; Liu (2011), Cluster synchronization in directed networks via intermittent pinning control on Neural, IEEE Trans Networks, 22, 1009, doi.org/10.1109/TNN.2011.2139224 ; Żochowski (2000), Intermittent dynamical control, Physica D, 145. ; Zhou (2008), Pinning adaptive synchronization of a general complex dynamical networks, Automatica, 44, 996, doi.org/10.1016/j.automatica.2007.08.016 ; Hu (2014), Cluster synchronization in directed networks of non - identical systems with noises via random pinning control, Physica A, 395. ; Lü (2013), Outer synchronization between uncertain complex networks based on backstepping design, Nonlinear Dynamics, 73. ; Li (2014), Finite - time synchronization for complex dynamical networks with hybrid coupling and time - varying delay, Nonlinear Dynamics, 76. ; Li (2009), Outer synchronization of coupled discrete - time networks, Chaos, 19, 013106, doi.org/10.1063/1.3068357 ; Wen (2014), Pinning synchronization of the drive and response dynamical networks with lag of Control, Archives Sciences, 24, 257. ; Williams (2000), Simple rules yield complex food webs, Nature, 404. ; Wang (2002), Synchronization in small - world dynamical networks of Bifurcation and, Chaos, 12, 187. ; Zhao (2011), Synchronization of dynamical networks with nonidentical nodes : criteria and control on Circuits and Systems, IEEE Trans, 58. ; Li (2013), IExponential synchronisation of united complex dynamical networks with multi - links via adaptive periodically intermittent control Theory and, IET Control Applications, 7, 1725, doi.org/10.1049/iet-cta.2013.0159 ; Watts (1998), Collective dynamics of small - world networks, Nature, 393. ; Pecora (1998), Master stability functions for synchronized coupled systems, Physical Review Letters, 10, 80. ; Zhang (2013), Parameter identification and synchronization of uncertain general complex networks via adaptive - impulsive control, Nonlinear Dynamics, 71, 353, doi.org/10.1007/s11071-012-0665-y ; Liang (2014), Synchronization in complex networks with non - delay and delay couplings via intermittent control with two switched periods, Physica A, 395. ; Yu (2007), Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification, Physica A, 375. ; Fan (2011), Synchronization between two complex dynamical networks using scalar signals under pinning control on Circuits and Systems, IEEE Trans, 57. ; Xia (2009), Pinning synchronization of delayed dynamical networks via periodically intermittent control, Chaos, 19, 013120, doi.org/10.1063/1.3071933 ; Girvan (2002), Community structure in social and biological networks of the National Academy of, Proc Sciences USA, 99. ; Li (2007), Synchronization between two ccoupled complex networks, Physical Review E, 76. ; Wu (2009), Generalized outer synchronization between complex dynamical networks, Chaos, 19, 013109, doi.org/10.1063/1.3072787 ; Gong (2012), Novel synchronization analysis for complex networks with hybrid coupling by handling multitude Kronecker product terms, Neurocomputing, 82. ; Hu (1994), Controlling spatiotemporal chaos in coupled map lattice systems, Physical Review Letters, 72, 68, doi.org/10.1103/PhysRevLett.72.68 ; Gong (2012), Pinning synchronization for a general complex networks with multiple time - varying coupling delays, Neural Processing Letters, 35, 221, doi.org/10.1007/s11063-012-9213-5 ; Wu (2008), Synchronization in complex dynamical networks with nonsymmetric coupling, Physica D, 19, 237. ; Liu (2010), Generalized synchronization in complex dynamical networks via adaptive couplings, Physica A, 389. ; Albert (1999), Diameter of the world wide web, Nature, 401. ; Zhang (2013), Synchronization for coupled neural networks with interval delay : a novel augmented LKF method on Neural Networks and Learning Systems, IEEE Trans, 24, 58. ; Tang (2008), Adaptive synchronization between two complex networks with nonidentical topological structures, Physica A, 387.