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Volumn 73, Issue 1-2, 2013, Pages 921-929

Observer-based synchronization in fractional-order leader-follower complex networks

Author keywords

Fractional order derivative; Leader follower network; Observer; Scalar synchronizing signal; Synchronization

Indexed keywords

COMPLEX DYNAMICAL NETWORKS; FRACTIONAL-ORDER DERIVATIVES; GLOBAL NETWORK SYNCHRONIZATION; LEADER-FOLLOWER; OBSERVER; OBSERVER-BASED SYNCHRONIZATIONS; SCALAR SYNCHRONIZING SIGNALS; SUFFICIENT CONDITIONS;

EID: 84879787514     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-0843-6     Document Type: Article
Times cited : (18)

References (49)
  • 3
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional Lorenz system
    • 34101 10.1103/PhysRevLett.91.034101
    • Grigorenko, I., Grigorenko, E.: Chaotic dynamics of the fractional Lorenz system. Phys. Rev. Lett. 91, 34101 (2003)
    • (2003) Phys. Rev. Lett. , vol.91
    • Grigorenko, I.1    Grigorenko, E.2
  • 4
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional Lü system
    • 10.1016/j.physa.2005.01.021
    • Deng, W.H., Li, C.P.: Chaos synchronization of the fractional Lü system. Physica A 353, 61-72 (2005)
    • (2005) Physica A , vol.353 , pp. 61-72
    • Deng, W.H.1    Li, C.P.2
  • 5
    • 37549042003 scopus 로고    scopus 로고
    • Unreliability of frequency-domain approximation in recognizing chaos in fractional-order systems
    • 10.1049/iet-spr:20070053
    • Tavazoei, M.S., Haeri, M.: Unreliability of frequency-domain approximation in recognizing chaos in fractional-order systems. IET Signal Process. 1, 171-181 (2007)
    • (2007) IET Signal Process. , vol.1 , pp. 171-181
    • Tavazoei, M.S.1    Haeri, M.2
  • 6
    • 51249088596 scopus 로고    scopus 로고
    • Chaotic attractors in incommensurate fractional order systems
    • 2514122 1157.26310 10.1016/j.physd.2008.03.037
    • Tavazoei, M.S., Haeri, M.: Chaotic attractors in incommensurate fractional order systems. Physica D 237, 2628-2637 (2008)
    • (2008) Physica D , vol.237 , pp. 2628-2637
    • Tavazoei, M.S.1    Haeri, M.2
  • 7
    • 37549047625 scopus 로고    scopus 로고
    • The evolution of chaotic dynamics for fractional unified system
    • 2398151 1217.37026 10.1016/j.physleta.2007.07.049
    • Deng, W., Li, C.P.: The evolution of chaotic dynamics for fractional unified system. Phys. Lett. A 372, 401-407 (2008)
    • (2008) Phys. Lett. A , vol.372 , pp. 401-407
    • Deng, W.1    Li, C.P.2
  • 8
    • 0037332868 scopus 로고    scopus 로고
    • Chaos in fractional-order autonomous nonlinear systems
    • 1033.37019 10.1016/S0960-0779(02)00438-1
    • Ahmad, W.M., Sprott, J.C.: Chaos in fractional-order autonomous nonlinear systems. Chaos Solitons Fractals 16, 339-351 (2003)
    • (2003) Chaos Solitons Fractals , vol.16 , pp. 339-351
    • Ahmad, W.M.1    Sprott, J.C.2
  • 9
    • 65249109832 scopus 로고    scopus 로고
    • Hyperchaos in the fractional-order Rössler system with lowest-order
    • 1170.34327 10.1142/S0218127409022890
    • Cafagna, D., Grassi, G.: Hyperchaos in the fractional-order Rössler system with lowest-order. Int. J. Bifurc. Chaos 19, 339-347 (2009)
    • (2009) Int. J. Bifurc. Chaos , vol.19 , pp. 339-347
    • Cafagna, D.1    Grassi, G.2
  • 10
    • 34247866598 scopus 로고    scopus 로고
    • Generalized synchronization in fractional order systems
    • 056201 10.1103/PhysRevE.75.056201
    • Deng, W.H.: Generalized synchronization in fractional order systems. Phys. Rev. E 75, 056201 (2007)
    • (2007) Phys. Rev. e , vol.75
    • Deng, W.H.1
  • 11
    • 82255185667 scopus 로고    scopus 로고
    • Adaptive synchronization of fractional-order chaotic systems via a single driving variable
    • 1242.93030 10.1007/s11071-011-9944-2
    • Zhang, R.X., Yang, S.P.: Adaptive synchronization of fractional-order chaotic systems via a single driving variable. Nonlinear Dyn. 66, 831-837 (2011)
    • (2011) Nonlinear Dyn. , vol.66 , pp. 831-837
    • Zhang, R.X.1    Yang, S.P.2
  • 12
    • 71849117613 scopus 로고    scopus 로고
    • Synchronization in coupled nonidentical incommensurate fractional-order systems
    • 1235.34159 10.1016/j.physleta.2009.10.051
    • Wang, J.-W., Zhang, Y.-B.: Synchronization in coupled nonidentical incommensurate fractional-order systems. Phys. Lett. A 374, 202-207 (2009)
    • (2009) Phys. Lett. A , vol.374 , pp. 202-207
    • Wang, J.-W.1    Zhang, Y.-B.2
  • 13
    • 27744554781 scopus 로고    scopus 로고
    • Chaos synchronization of the Chua system with a fractional order
    • 2186261 10.1016/j.physa.2005.06.078
    • Li, C.P., Deng, W.H., Xu, D.: Chaos synchronization of the Chua system with a fractional order. Physica A 360, 171-185 (2006)
    • (2006) Physica A , vol.360 , pp. 171-185
    • Li, C.P.1    Deng, W.H.2    Xu, D.3
  • 14
    • 65749088733 scopus 로고    scopus 로고
    • Synchronization of a new fractional-order hyperchaotic system
    • 2533122 1231.34091 10.1016/j.physleta.2009.04.063
    • Wu, X.J., Lu, H.T., Shen, S.L.: Synchronization of a new fractional-order hyperchaotic system. Phys. Lett. A 373, 2329-2337 (2009)
    • (2009) Phys. Lett. A , vol.373 , pp. 2329-2337
    • Wu, X.J.1    Lu, H.T.2    Shen, S.L.3
  • 15
    • 80051510187 scopus 로고    scopus 로고
    • Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control
    • 10.1109/TFUZZ.2011.2127482
    • Lin, T.-C., Lee, T.-Y.: Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control. IEEE Trans. Fuzzy Syst. 19, 623-635 (2011)
    • (2011) IEEE Trans. Fuzzy Syst. , vol.19 , pp. 623-635
    • Lin, T.-C.1    Lee, T.-Y.2
  • 16
    • 84866136226 scopus 로고    scopus 로고
    • Nonlinear state-observer control for projective synchronization of a fractional-order hyperchaotic system
    • 2945530 1263.34011 10.1007/s11071-012-0397-z
    • Liu, L., Liang, D.L., Liu, C.: Nonlinear state-observer control for projective synchronization of a fractional-order hyperchaotic system. Nonlinear Dyn. 69, 1929-1939 (2012)
    • (2012) Nonlinear Dyn. , vol.69 , pp. 1929-1939
    • Liu, L.1    Liang, D.L.2    Liu, C.3
  • 17
    • 79955841657 scopus 로고    scopus 로고
    • Observer-based synchronization for a class of fractional chaotic systems via a scalar signal: Results involving the exact solution of the error dynamics
    • 2803333 1215.34072 10.1142/S021812741102874X
    • Cafagna, D., Grassi, G.: Observer-based synchronization for a class of fractional chaotic systems via a scalar signal: results involving the exact solution of the error dynamics. Int. J. Bifurc. Chaos 21, 955-962 (2011)
    • (2011) Int. J. Bifurc. Chaos , vol.21 , pp. 955-962
    • Cafagna, D.1    Grassi, G.2
  • 18
    • 84858706326 scopus 로고    scopus 로고
    • Observer-based projective synchronization of fractional systems via a scalar signal: Application to hyperchaotic Rössler systems
    • 2904161 1243.93047 10.1007/s11071-011-0208-y
    • Cafagna, D., Grassi, G.: Observer-based projective synchronization of fractional systems via a scalar signal: application to hyperchaotic Rössler systems. Nonlinear Dyn. 68, 117-128 (2012)
    • (2012) Nonlinear Dyn. , vol.68 , pp. 117-128
    • Cafagna, D.1    Grassi, G.2
  • 19
    • 0035826155 scopus 로고    scopus 로고
    • Exploring complex networks
    • 10.1038/35065725
    • Strogatz, S.H.: Exploring complex networks. Nature 410, 268-276 (2001)
    • (2001) Nature , vol.410 , pp. 268-276
    • Strogatz, S.H.1
  • 20
    • 0036340313 scopus 로고    scopus 로고
    • Synchronization in small-world dynamical networks
    • 10.1142/S0218127402004292
    • Wang, X.F., Chen, G.R.: Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos 12, 187-192 (2002)
    • (2002) Int. J. Bifurc. Chaos , vol.12 , pp. 187-192
    • Wang, X.F.1    Chen, G.R.2
  • 21
    • 0038396314 scopus 로고    scopus 로고
    • General stability analysis of synchronized dynamics in coupled systems
    • 026209 10.1103/PhysRevE.67.026209
    • Chen, Y.H., Rangarajan, G., Ding, M.Z.: General stability analysis of synchronized dynamics in coupled systems. Phys. Rev. E 67, 026209 (2003)
    • (2003) Phys. Rev. e , vol.67
    • Chen, Y.H.1    Rangarajan, G.2    Ding, M.Z.3
  • 22
    • 27244458075 scopus 로고    scopus 로고
    • Clustering and the synchronization of oscillator networks
    • 015101 2178368 10.1103/PhysRevE.72.015101
    • McGraw, P.N., Menzinger, M.: Clustering and the synchronization of oscillator networks. Phys. Rev. E 72, 015101 (2005)
    • (2005) Phys. Rev. e , vol.72
    • McGraw, P.N.1    Menzinger, M.2
  • 23
    • 79953282866 scopus 로고    scopus 로고
    • Mixed outer synchronization of coupled complex networks with time-varying coupling delay
    • 013121 2808176 10.1063/1.3555836
    • Wang, J.W., Ma, Q.H., Zeng, L., Abd-Elouahab, M.S.: Mixed outer synchronization of coupled complex networks with time-varying coupling delay. Chaos 21, 013121 (2011)
    • (2011) Chaos , vol.21
    • Wang, J.W.1    Ma, Q.H.2    Zeng, L.3    Abd-Elouahab, M.S.4
  • 24
    • 80455160347 scopus 로고    scopus 로고
    • Synchronization in lattice-embedded scale-free networks
    • 10.1016/j.physa.2011.08.012
    • Tauro, C.B., Tamarit, F.A., Gleiser, P.M.: Synchronization in lattice-embedded scale-free networks. Physica A 391, 834-842 (2012)
    • (2012) Physica A , vol.391 , pp. 834-842
    • Tauro, C.B.1    Tamarit, F.A.2    Gleiser, P.M.3
  • 25
    • 27744462122 scopus 로고    scopus 로고
    • Synchronization in fractional-order differential systems
    • 2186154 1094.34034 10.1016/j.physd.2005.09.012
    • Zhou, T.S., Li, C.P.: Synchronization in fractional-order differential systems. Physica D 212, 111-125 (2005)
    • (2005) Physica D , vol.212 , pp. 111-125
    • Zhou, T.S.1    Li, C.P.2
  • 26
    • 63449084428 scopus 로고    scopus 로고
    • Pinning control of fractional-order weighted complex networks
    • 013112 2513760 10.1063/1.3068350
    • Tang, Y., Wang, Z., Fang, J.: Pinning control of fractional-order weighted complex networks. Chaos 19, 013112 (2009)
    • (2009) Chaos , vol.19
    • Tang, Y.1    Wang, Z.2    Fang, J.3
  • 27
    • 77649232335 scopus 로고    scopus 로고
    • Network synchronization in a population of star-coupled fractional nonlinear oscillators
    • 1236.05188 10.1016/j.physleta.2010.01.042
    • Wang, J.W., Zhang, Y.B.: Network synchronization in a population of star-coupled fractional nonlinear oscillators. Phys. Lett. A 374, 1464-1468 (2010)
    • (2010) Phys. Lett. A , vol.374 , pp. 1464-1468
    • Wang, J.W.1    Zhang, Y.B.2
  • 28
    • 84863213609 scopus 로고    scopus 로고
    • Cluster synchronization in fractional-order complex dynamical networks
    • 06179543 10.1016/j.physleta.2012.05.060
    • Chen, L.P., Chai, Y., Wu, R.C., Sun, J., Ma, T.D.: Cluster synchronization in fractional-order complex dynamical networks. Phys. Lett. A 376, 2381-2388 (2012)
    • (2012) Phys. Lett. A , vol.376 , pp. 2381-2388
    • Chen, L.P.1    Chai, Y.2    Wu, R.C.3    Sun, J.4    Ma, T.D.5
  • 29
    • 79953707328 scopus 로고    scopus 로고
    • Synchronization of N-coupled incommensurate fractional-order chaotic systems with ring connection
    • 2787826 1225.34059 10.1016/j.cnsns.2010.12.035
    • Delshad, S.S., Asheghan, M.M., Beheshti, M.H.: Synchronization of N-coupled incommensurate fractional-order chaotic systems with ring connection. Commun. Nonlinear Sci. Numer. Simul. 16, 3815-3824 (2011)
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , pp. 3815-3824
    • Delshad, S.S.1    Asheghan, M.M.2    Beheshti, M.H.3
  • 30
    • 84862937075 scopus 로고    scopus 로고
    • Convergence speed of a fractional order consensus algorithm over undirected scale-free network
    • 2869897 1263.93013 10.1002/asjc.390
    • Sun, W., Li, Y., Li, C., Chen, Y.: Convergence speed of a fractional order consensus algorithm over undirected scale-free network. Asian J. Control 13, 936-946 (2011)
    • (2011) Asian J. Control , vol.13 , pp. 936-946
    • Sun, W.1    Li, Y.2    Li, C.3    Chen, Y.4
  • 31
    • 80053433381 scopus 로고    scopus 로고
    • Robust outer synchronization between two complex networks with fractional order dynamics
    • 033121 10.1063/1.3629986
    • Asheghan, M.M., Míguez, J., Hamidi-Beheshti, M.T., Tavazoei, M.S.: Robust outer synchronization between two complex networks with fractional order dynamics. Chaos 21, 033121 (2011)
    • (2011) Chaos , vol.21
    • Asheghan, M.M.1    Míguez, J.2    Hamidi-Beheshti, M.T.3    Tavazoei, M.S.4
  • 32
    • 84863443522 scopus 로고    scopus 로고
    • A general fractional-order dynamical network: Synchronization behavior and state tuning
    • 023102 10.1063/1.3701726
    • Wang, J.W., Xiong, X.H.: A general fractional-order dynamical network: synchronization behavior and state tuning. Chaos 22, 023102 (2012)
    • (2012) Chaos , vol.22
    • Wang, J.W.1    Xiong, X.H.2
  • 33
    • 67649626081 scopus 로고    scopus 로고
    • Mittag-Leffler stability of fractional order nonlinear dynamic systems
    • 2879525 1185.93062 10.1016/j.automatica.2009.04.003
    • Li, Y., Chen, Y.Q., Podlubny, I.: Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45, 1965-1969 (2009)
    • (2009) Automatica , vol.45 , pp. 1965-1969
    • Li, Y.1    Chen, Y.Q.2    Podlubny, I.3
  • 34
    • 78149469035 scopus 로고    scopus 로고
    • Synchronization between two complex dynamical networks using scalar signals under pinning control
    • 2788985 10.1109/TCSI.2010.2048774
    • Fan, C.-X., Jiang, G.-P., Jiang, F.-H.: Synchronization between two complex dynamical networks using scalar signals under pinning control. IEEE Trans. Circuits Syst. I, Regul. Pap. 57, 2991-2998 (2010)
    • (2010) IEEE Trans. Circuits Syst. I, Regul. Pap. , vol.57 , pp. 2991-2998
    • Fan, C.-X.1    Jiang, G.-P.2    Jiang, F.-H.3
  • 36
    • 19144371559 scopus 로고    scopus 로고
    • Chaotic dynamics and synchronization of fractional-order Arneodo's systems
    • 1074.65146 10.1016/j.chaos.2005.02.023
    • Lu, J.G.: Chaotic dynamics and synchronization of fractional-order Arneodo's systems. Chaos Solitons Fractals 26, 1125-1133 (2005)
    • (2005) Chaos Solitons Fractals , vol.26 , pp. 1125-1133
    • Lu, J.G.1
  • 38
    • 84870974905 scopus 로고    scopus 로고
    • On the simplest fractional-order memristor-based chaotic system
    • 2992125 10.1007/s11071-012-0522-z
    • Cafagna, D., Grassi, G.: On the simplest fractional-order memristor-based chaotic system. Nonlinear Dyn. 70, 1185-1197 (2012)
    • (2012) Nonlinear Dyn. , vol.70 , pp. 1185-1197
    • Cafagna, D.1    Grassi, G.2
  • 39
    • 0029358909 scopus 로고
    • Synchronization in an array of linearly coupled dynamical systems
    • 1351879 0867.93042 10.1109/81.404047
    • Wu, C.W., Chua, L.O.: Synchronization in an array of linearly coupled dynamical systems. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 42, 430-447 (1995)
    • (1995) IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. , vol.42 , pp. 430-447
    • Wu, C.W.1    Chua, L.O.2
  • 42
    • 74149090385 scopus 로고    scopus 로고
    • Analytic study on linear systems of fractional differential equations
    • 2579481 1189.34017 10.1016/j.camwa.2009.06.035
    • Odibat, Z.M.: Analytic study on linear systems of fractional differential equations. Comput. Math. Appl. 59, 1171-1183 (2010)
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1171-1183
    • Odibat, Z.M.1
  • 43
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in the fractional-order Rössler equations
    • 2092674 10.1016/j.physa.2004.04.113
    • Li, C.G., Chen, G.R.: Chaos and hyperchaos in the fractional-order Rössler equations. Physica A 341, 55-61 (2004)
    • (2004) Physica A , vol.341 , pp. 55-61
    • Li, C.G.1    Chen, G.R.2
  • 44
    • 1442354755 scopus 로고    scopus 로고
    • Synchronization of fractional order chaotic systems
    • 067203 10.1103/PhysRevE.68.067203
    • Li, C.G., Liao, X.F., Yu, J.B.: Synchronization of fractional order chaotic systems. Phys. Rev. E 68, 067203 (2003)
    • (2003) Phys. Rev. e , vol.68
    • Li, C.G.1    Liao, X.F.2    Yu, J.B.3
  • 45
    • 22844431613 scopus 로고    scopus 로고
    • Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal
    • 1086.94007 10.1016/j.chaos.2005.04.032
    • Lu, J.G.: Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal. Chaos Solitons Fractals 27, 519-525 (2006)
    • (2006) Chaos Solitons Fractals , vol.27 , pp. 519-525
    • Lu, J.G.1
  • 46
    • 34347330038 scopus 로고    scopus 로고
    • A necessary condition for double scroll attractor existence in fractional order systems
    • 1209.37037 10.1016/j.physleta.2007.05.081
    • Tavazoei, M.S., Haeri, M.: A necessary condition for double scroll attractor existence in fractional order systems. Phys. Lett. A 367, 102-113 (2007)
    • (2007) Phys. Lett. A , vol.367 , pp. 102-113
    • Tavazoei, M.S.1    Haeri, M.2
  • 47
    • 67649624652 scopus 로고    scopus 로고
    • Stability preservation analysis for frequency-based methods in numerical simulation of fractional order systems
    • 2475942 10.1137/080715949
    • Tavazoei, M.S., Haeri, M., Bolouki, S., Siami, M.: Stability preservation analysis for frequency-based methods in numerical simulation of fractional order systems. SIAM J. Numer. Anal. 47(1), 321-338 (2008)
    • (2008) SIAM J. Numer. Anal. , vol.47 , Issue.1 , pp. 321-338
    • Tavazoei, M.S.1    Haeri, M.2    Bolouki, S.3    Siami, M.4
  • 48
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • 1926466 1009.65049 10.1023/A:1016592219341
    • Diethelm, K., Ford, N.J., Freed, A.D.: A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29, 3-22 (2002)
    • (2002) Nonlinear Dyn. , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 49
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • 1876137 1014.34003 10.1006/jmaa.2000.7194
    • Diethelm, K., Ford, N.J.: Analysis of fractional differential equations. J. Math. Anal. Appl. 265, 229-248 (2002)
    • (2002) J. Math. Anal. Appl. , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2


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