Finite-time synchronization of complex networks with nonidentical discontinuous nodes

Nonlinear Dynamics

Volumn 73, Issue 4, 2013, Pages 2313-2327

  Yang, Xinsong ^a   Wu, Zhiyou ^a   Cao, Jinde ^b  

^a CHONGQING NORMAL UNIVERSITY   (China)

^b SOUTHEAST UNIVERSITY   (China)

Author keywords

Asymmetric coupling; Complex network; Discontinuous chaotic system; Finite time synchronization

Indexed keywords

ASYMMETRIC COUPLING; DISCONTINUOUS FUNCTIONS; FINITE TIME STABILITY; FINITE-TIME SYNCHRONIZATIONS; INEQUALITY TECHNIQUES; NON-IDENTICAL; NON-IDENTICAL NODES; SCALE FREE NETWORKS;

CHAOTIC SYSTEMS; COMPLEX NETWORKS;

SYNCHRONIZATION;

EID: 84882439981     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-0942-4     Document Type: Article

References (49)

1. Danca, M.: Controlling chaos in discontinuous dynamical systems. Chaos Solitons Fractals 22, 605-612 (2004)
2. Forti, M., Grazzini, M., Nistri, P., Pancioni, L.: Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Phys. D, Nonlinear Phenom. 214(1), 88-99 (2006)
3. Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Kluwer Academic, Dordrecht (1988)
4. Wu, Z.-G., Shi, P., Su, H., Chu, J.: Passivity analysis for discrete-time stochastic Markovian jump neural networks with mixed time delays. IEEE Trans. Neural Netw. 22(10), 1566-1575 (2011)
5. Yang, X., Cao, J., Lu, J.: Synchronization of randomly coupled neural networks with Markovian jumping and time-delay. IEEE Trans. Circuits Syst. I 60(2), 363-376 (2013)
6. Aubin, J.P., Cellina, A.: Differential Inclusions. Springer, Berlin (1984)
7. Cai, Z., Huang, L.: Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations. Neurocomputing 74, 3170-3179 (2011)
8. Liu, J., Liu, X., Xie, W.: Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations. Inf. Sci. 183, 92-105 (2012)
9. Forti, M., Nistri, P., Papini, D.: Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans. Neural Netw. 16(6), 1449-1463 (2005)
10. Hui, Q., Haddad, W.M., Bhat, S.P.: Finite-time semistability and consensus for nonlinear dynamical networks. IEEE Trans. Autom. Control 53(8), 1887-1900 (2008)
11. Yang, X., Cao, J.: Finite-time stochastic synchronization of complex networks. Appl. Math. Model. 34(11), 3631-3641 (2010)
12. Adamic, L.A., Huberman, B.A.: Growth dynamics of the world wide web. Nature 401(6749), 131 (1999)
13. Strogatz, S.H., Stewart, I.: Coupled oscillators and biological synchronization. Sci. Am. 269(6), 102-109 (1993)
14. Wu, Z., Park, J., Su, H., Chu, J.: Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data. Nonlinear Dyn. 69(4), 2021-2030 (2012)
15. Chen, D., Zhang, R., Ma, X., Liu, S.: Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme. Nonlinear Dyn. 69(1-2), 35-55 (2012)
16. Yang, X., Cao, J., Lu, J.: Synchronization of delayed complex dynamical networks with impulsive and stochastic effects. Nonlinear Anal., Real World Appl. 12, 2252-2266 (2011)
17. Liao, T.L., Huang, N.S.: An observer-based approach for chaotic synchronization with applications to secure communications. IEEE Trans. Circuits Syst. I 46(9), 1144-1150 (1999)
18. Wu, Z.-G., Shi, P., Su, H., Chu, J.: Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data. IEEE Trans. Cybern. doi: 10.1109/TSMCB.2012.2230441
19. Dimassi, H., Loría, A., Belghith, S.: A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers. Commun. Nonlinear Sci. Numer. Simul. 17, 3727-3739 (2012)
20. Yang, X., Cao, J.: Stochastic synchronization of coupled neural networks with intermittent control. Phys. Lett. A 373(36), 3259-3272 (2009)
21. Lü, L., Meng, L.: Parameter identification and synchronization of spatiotemporal chaos in uncertain complex network. Nonlinear Dyn. 66(4), 289-295 (2011)
22. Lu, J., Kurths, J., Cao, J., Mahdavi, N., Huang, C.: Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans. Neural Netw. Learn. Syst. 23(2), 285-292 (2012)
23. Yang, X., Cao, J., Lu, J.: Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths. IEEE Trans. Neural Netw. Learn. Syst. 23(1), 60-71 (2012)
24. Batista, C.A.S., Lopes, S.R., Viana, R.L., Batista, A.M.: Delayed feedback control of bursting synchronization in a scale-free neuronal network. Neural Netw. 23(1), 114-124 (2010)
25. Li, Z., Chen, G.: Global synchronization and asymptotic stability of complex dynamical networks. IEEE Trans. Circuits Syst. II 53(1), 28-33 (2006)
26. Yang, X., Cao, J., Long, Y., Rui, W.: Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations. IEEE Trans. Neural Netw. 21(10), 1656-1667 (2010)
27. Chen, T., Liu, X., Lu, W.: Pinning complex networks by a single controller. IEEE Trans. Circuits Syst. I 54(6), 1317-1326 (2007)
28. Cai, N., Li, W., Jing, Y.: Finite-time generalized synchronization of chaotic systems with different order. Nonlinear Dyn. 64(4), 385-393 (2011)
29. Shen, J., Cao, J.: Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn. Neurodyn. 5(4), 373-385 (2011)
30. Kwon, O.M., Park, J.H., Lee, S.M.: Secure communication based on chaotic synchronization via interval time-varying delay feedback control. Nonlinear Dyn. 63(1-2), 239-252 (2011)
31. Liu, X., Chen, T., Cao, J., Lu, W.: Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Netw. 24(10), 1013-1021 (2011)
32. Liu, X., Cao, J., Yu, W.: Filippov systems and quasi-synchronization control for switched networks. Chaos 22(3), 033110 (2012)
33. Liu, X., Yu, W.: Quasi-synchronization of delayed coupled networks with non-identical discontinuous nodes. Adv. Neural Netw. 2012, 274-284 (2012)
34. Liu, B., Lu, W., Chen, T.: New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides. Neural Netw. 25, 5-13 (2012)
35. Yang, X., Cao, J.: Exponential synchronization of delayed neural networks with discontinuous activations. IEEE Trans. Circuits Syst. I. doi: 10.1109/TCSI.2013.2244451
36. Cortés, J.: Finite-time convergent gradient flows with applications to network consensus. Automatica 42(11), 1993-2000 (2006)
37. Xiao, F., Wang, L., Chen, J., Gao, Y.: Finite-time formation control for multi-agent systems. Automatica 45(11), 2605-2611 (2009)
38. Wang, L., Xiao, F.: Finite-time consensus problems for networks of dynamic agents. IEEE Trans. Autom. Control 55(4), 950-955 (2010)
39. Yang, X., Cao, J., Lu, J.: Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control. IEEE Trans. Circuits Syst. I 59(2), 371-384 (2012)
40. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509-512 (1999)
41. Forti, M., Nistri, P.: Global convergence of neural networks with discontinuous neuron activations. IEEE Trans. Circuits Syst. I 50(11), 1421-1435 (2003)
42. Sprott, J.C.: A new class of chaotic circuit. Phys. Lett. A 266(1), 19-23 (2000)
43. Brown, R.: Generalizations of the Chua equations. IEEE Trans. Circuits Syst. I 40(11), 878-884 (1993)
44. Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9(07), 1465-1466 (1999)
45. Zhou, J., Chen, T., Xiang, L.: Adaptive synchronization of coupled chaotic delayed systems based on parameter identification and its applications. Int. J. Bifurc. Chaos 16(10), 2923-2933 (2006)
46. Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1988)
47. Clarke, F.H.: Optimization and Nonsmooth Analysis, vol. 5. SIAM, Philadelphia (1987)
48. Paden, B., Sastry, S.: A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators. IEEE Trans. Circuits Syst. 34(1), 73-82 (1987)
49. Yang, X., Zhu, Q., Huang, C.: Lag stochastic synchronization of chaotic mixed time-delayed neural networks with uncertain parameters or perturbations. Neurocomputing 74(10), 1617-1625 (2011)