Pinning synchronization of the drive and response dynamical networks with lag

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Abstract

This paper investigates the pinning synchronization of two general complex dynamical networks with lag. The coupling configuration matrices in the two networks are not need to be symmetric or irreducible. Several convenient and useful criteria for lag synchronization are obtained based on the lemma of Schur complement and the Lyapunov stability theory. Especially, the minimum number of controllers in pinning control can be easily obtained. At last, numerical simulations are provided to verify the effectiveness of the criteria

[1] D.J. WATTS and S.H. STROGATZ: Collective dynamics of ‘small-word’ networks. Nature, 393 (1998), 440-442.

[2] M. GIRVAN and M.E.J. NEWMAN: Community structure in social and biological networks. Proc. of the National Academy of Sciences USA, 99 (2002), 7821-7826.

[3] R. ALBERT, H. JEONG and A.L. BARABÁSI: Diameter of the world-wide web. Nature, 401 (1999), 130-131.

[4] R.J. WILLIAMS and N.D. MARTINEZ: Simple rules yield complex food webs. Nature, 404 (2000), 180-183.

[5] P. ERDÖS and A. RÉNYI: On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 5 (1960), 17-61.

[6] E. ALMAAS, R.V. KULKARNI and D. STOUD: Characterizing the structure of small-world networks. Physical Review Letters, 88 (2002), 098101.1-4.

[7] A.L. BARABÁSI and R. ALBERT: Emergence of scaling in random networks. Science, 286 (1999), 509-512.

[8] A.L. BARABÁSI, R. ALBERT and H. JEONG: Mean-field theory for scale-free random networks. J. of Physics A, 272 (1999), 173-187.

[9] Y. FAN, Y. WANG, Y. ZHANG and Q. WANG: Robust synchronization control for complex networks with disturbed sampling couplings. Applied Mathematics and Computation, 219 (2013), 6719U˝ 6728.

[10] F. NIAN, X. WANG, Y. NIU and D. LIN: Module-phase synchronization in complex dynamic system. Applied Mathematics and Computation, 217 (2010), 2481-2489.

[11] D. GHOSH: Projective-dual synchronization in delay dynamical systems with timevarying coupling delay. Nonlinear Dynamics, 66 (2011), 717-730.

[12] P. RAO, Z. WU and M. LIU: Adaptive projective synchronization of dynamical networks with distributed time delays. Nonlinear Dynamics, 67 (2012), 1729-1736.

[13] H. DU, P. SHI and N. LU: Function projective synchronization in complex networks with time delay via hybrid feedback control. Nonlinear Analysis: RealWorld Applications, 14 (2013), 1182-1190.

[14] S. ZHENG, G. DONG and Q. BI: Impulsive synchronization of complex networks with non-delayed and delayed coupling. Physics Letters A, 373 (2009), 4255-4259.

[15] K. LI and C. LAI: Adaptive impulsive synchronization of uncertain complex dynamical networks. Physics Letters A, 372 (2008), 1601-1606.

[16] J. LU, D.W.C. HO, J. CAO and J. KURTHS: Single impulse controller for global exponential synchronization of dynamical networks. Nonlinear Analysis: Real World Applications, 14 (2013), 581-593.

[17] K. WANG, X. FU and K. LI: Cluster synchronization in community networks with nonidentical nodes. Chaos, 19 (2009), 023106.1-023106.10.

[18] E. GUIREY, M. BEES, A. MARTIN and M. SROKOSZ: Persistence of cluster synchronization under the influence of advection. Physics Review E, 81 (2010), 051902.1-059102.16.

[19] W. LU, B. LIU and T. CHEN: Cluster synchronization in networks of coupled nonidentical dynamical systems. Chaos, 20 (2010), 013120.1-013120.12.

[20] J. ZHOU, J.LU and J. LÜ: Pinning adaptive synchronization of a general complex dynamical network. Automatica, 44 (2008) 996-1003.

[21] C. FAN, G. JIANG and F. JIANG: Synchronization between two complex dynamical networks using scalar signals under pinning control. IEEE Trans. on Circuits Systems I, 57 (2011) 2991-2998.

[22] Y.Z. SUN. W. LI and J. RUAN: Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation. Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 989-998.

[23] Q. MIAO, Y. TANG, S. LU and J. FANG: Lag synchronization of a class of chaotic systems with unkown parameters. Nonlinear Dynamics, 57 (2009), 107-112.

[24] G. HU and Z. QU: Controlling spatiotemporal chaos in coupled map lattice systems. Physical Review Letters, 72 (1994), 68-71.

[25] X. JIN and G. YANG: Adaptive pinning synchronization of a class of nonlinearly coupled complex networks. Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 316-326.

[26] W. GUO: Lag synchronization of complex networks via pin ning control. Nonlinear Analysis: Real World Applications, 12 (2011), 2579-2585.

[27] W. YU and J. CAO: Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification. Physics A, 375 (2007), 467-482.

[28] S. BOYED, L.E. GHAOUI, E. FERON and V. BALAKRISHNAN: Linear matrix inequalities in system and control theory. Philadelphia, PA:SIAM, 1994.

[29] J. ZHOU, J. LU and J. LÜ: Erratum to:"Pinning adaptive synchronization of a general complex dynamical network". [Automatica, 44 (2008), 996-1003], Automatica, 45 (2009), 598-599.

[30] J. LU, D.W.C. HO: Stability of complex dynamical networks with noise disturbance under performance constant. Nonlinear Analysis: Real World Applications, 12 (2011), 1974-1984.

[31] W. LU and T. CHEN: Synchronization of coupled connected neural networks with delays. IEEE Trans. on Circuits and Systems, 51 (2004), 2491-2503.

Archives of Control Sciences

The Journal of Polish Academy of Sciences

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IMPACT FACTOR 2016: 0.705

CiteScore 2016: 3.11

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.565

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