Effect of the coupling matrix with a weight parameter on synchronization pattern in a globally coupled network

Nonlinear Dynamics

Volumn 74, Issue 1-2, 2013, Pages 55-64

  Ma, Zhongjun ^a   Zhang, Suzhang ^a   Jiang, Guirong ^a   Li, Kezan ^a  

^a GUILIN UNIVERSITY OF ELECTRONIC TECHNOLOGY   (China)

Author keywords

Cluster synchronization; Full synchronization; Synchronization bifurcation; Synchronization pattern

Indexed keywords

CLUSTER SYNCHRONIZATION; COUPLED NETWORKS; COUPLING MATRIX; COUPLING STRENGTHS; NUMBER OF CLUSTERS; SYNCHRONIZATION MANIFOLDS; SYNCHRONIZATION PATTERNS; WEIGHT PARAMETERS;

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; NUMERICAL MODELS;

SYNCHRONIZATION;

EID: 84883821669     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-0948-y     Document Type: Article

References (24)

1. Wang, X.F.; Chen, G.R.: Complex networks: small-world, scale-free and beyond. IEEE Circuits Syst. Mag. 3, 6-20 (2003)
2. Arenas, A.; Guilera, A.D.; Kurths, J.; Moreno, Y.; Zhou, C.S.: Synchronization in complex networks. Phys. Rep. 469, 93-143 (2008)
3. Yu, W.W.; Chen, G.R.; Lü, J.H.: On pinning synchronization of complex dynamical networks. Automatica 45, 429-435 (2009)
4. Chen, J.R.; Jiao, L.C.; Wu, J.S.; Wang, X.D.: Projective synchronization with different scale factors in a driven-response complex network and its application in image encryption. Nonlinear Anal.; Real World Appl. 11, 3045-3058 (2010)
5. Sun, W.; Chen, Z.; Lü, J.H.; Chen, S.H.: Outer synchronization of complex networks with delay via impulse. Nonlinear Dyn. (2012). doi: 10.1007/s11071-012-0383-5
6. Wang, J.L.; Wu, H.N.: Synchronization criteria for impulsive complex dynamical networks with time-varying delay. Nonlinear Dyn. (2012). doi: 10.1007/s11071-012-0427-x
7. Belykh, V.N.; Osipov, G.V.; Petrov, V.S.; Suykens, J.A.K.; Vandewalle, J.: Cluster synchronization in oscillatory networks. Chaos 18, 037106 (2008)
8. Pogromsky, A.Y.: A partial synchronization theorem. Chaos 18, 037107 (2008)
9. Ma, Z.J.; Liu, Z.R.; Zhang, G.: A new method to realize cluster synchronization in connected chaotic networks. Chaos 16, 023103 (2006) (Pubitemid 44000320)
10. Ma, Z.J.; Zhang, G.; Wang, Y.; Liu, Z.R.: Cluster synchronization in star-like complex networks. J. Phys. A, Math. Theor. 41, 155101 (2008)
11. Huang, L.; Park, K.; Lai, Y.C.; Yang, L.; Yang, K.Q.: Abnormal synchronization in complex clustered networks. Phys. Rev. Lett. 97, 164101 (2006) (Pubitemid 44601543)
12. Zhou, J.; Chen, T.P.; Xiang, L.: Adaptive synchronization of coupled chaotic systems based on parameters identification and its applications. Int. J. Bifurc. Chaos 16, 2923-2933 (2006) (Pubitemid 44924970)
13. Belykh, V.N.; Belykh, I.V.; Hasler, M.: Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems. Phys. Rev. E 62(5), 6332-6345 (2000) (Pubitemid 32033313)
14. Belykh, V.N.; Belykh, I.V.; Hasler, M.: Connected graph stability method for synchronized coupled chaotic systems. Physica D 195, 159-187 (2004)
15. Liu, B.; Lu, W.L.; Chen, T.P.: New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides. Neural Netw. 25, 5-13 (2012)
16. Wu, W.; Chen, T.P.: Partial synchronization in linearly and symmetrically coupled ordinary differential systems. Physica D 238, 355-364 (2009)
17. Belykh, V.N.; Belykh, I.V.; Nevidin, K.; Hasler, M.: Persistent clusters in lattices of coupled nonidentical chaotic systems. Chaos 13, 165-178 (2003) (Pubitemid 36419915)
18. Belykh, V.N.; Belykh, I.V.; Hasler, M.; Nevidin, K.V.: Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators. Int. J. Bifurc. Chaos 13, 755-779 (2003) (Pubitemid 36739287)
19. Wang, X.F.; Chen, G.R.: Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos 12, 187-192 (2002) (Pubitemid 34862071)
20. Wang, X.F.; Chen, G.R.: Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circuits Syst. I 49, 54-62 (2002) (Pubitemid 34231903)
21. Lü, J.H.; Yu, X.H.; Chen, G.R.: Chaos synchronization of general complex dynamical networks. Physica A 334, 281-302 (2004)
22. Golubitsky, M.; Stewart, I.; Török, A.: Patterns of synchrony in coupled cell networks with multiple arrows. SIAM J. Appl. Dyn. Syst. 4(1), 78-100 (2005) (Pubitemid 43385187)
23. Golubitsky, M.; Stewart, I.: Nonlinear dynamics of networks: the groupoid formalism. Bull. Am. Math. Soc. 43(3), 305-364 (2006) (Pubitemid 44002571)
24. Shil'nikov, L.P.: Chua's circuit: rigorous results and future problems. Int. J. Bifurc. Chaos 4, 784-786 (1993)