Finite-time synchronization of coupled neural networks via discontinuous controllers

Cognitive Neurodynamics

Volumn 5, Issue 4, 2011, Pages 373-385

  Shen, Jun ^a   Cao, Jinde ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

Discontinuous control; Finite time synchronization; Neural networks; Pinning control

Indexed keywords

ARTICLE; CELL SYNCHRONIZATION; NERVE CELL NETWORK; TUNING CURVE;

EID: 81355138765     PISSN: 18714080     EISSN: 18714099     Source Type: Journal    
DOI: 10.1007/s11571-011-9163-z     Document Type: Article

References (30)

1. Aubin JP (1991) Viability theory. Birkhauser, Boston
2. J Cao J Lu 2006 Adaptive synchronization of neural networks with or without time-varying delay Chaos 16 1 013133 16599764 10.1063/1.2178448 (Pubitemid 43528813)
3. J Cao Q Song 2006 Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays Nonlinearity 19 7 1601 1617 10.1088/0951-7715/19/7/008 (Pubitemid 43941157)
4. J Cao G Chen P Li 2008 Global synchronization in an array of delayed neural networks with hybrid coupling IEEE Trans Syst Man Cybern B 38 2 488 498 10.1109/TSMCB.2007.914705 (Pubitemid 351479567)
5. Y Chen JH Lü 2009 Finite-time synchronization of complex dynamical networks J Syst Sci Complex 29 10 1419 1430
6. G Chen J Zhou Z Liu 2004 Global synchronization of coupled delayed neural networks and applications to chaotic CNN models Int J Bifurcat Chaos 14 7 2229 2240 10.1142/S0218127404010655 (Pubitemid 40242101)
7. T Chen X Liu W Lu 2007 Pinning complex networks by a single controller IEEE Trans Circuits Syst I Regul Pap 54 6 1317 1326 10.1109/TCSI.2007.895383 (Pubitemid 46971536)
8. J Cortés 2006 Finite-time convergent gradient flows with applications to network consensus Automatica 42 11 1993 2000 10.1016/j.automatica.2006.06.015 (Pubitemid 44436061)
9. J Cortés 2008 Discontinuous dynamical systems: A tutorial on solutions, nonsmooth analysis, and stability IEEE Control Syst Mag 28 3 36 73 10.1109/MCS.2008.919306 (Pubitemid 351784780)
10. M Forti M Grazzini P Nistri L Pancioni 2006 Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations Physica D Nonlinear Phenomena 214 1 88 99 10.1016/j.physd.2005.12. 006 (Pubitemid 43131061)
11. Gupta MM, Jin L, Homma N (2003) Static and dynamic neural networks. Wiley-Interscience, New York
12. Hardy GH, Littlewood JE, Pólya G (1988) Inequalities. Cambridge University Press, Cambridge
13. Horn RA, Johnson CR (1990) Matrix Analysis. Cambridge University Press, Cambridge
14. Q Hui WM Haddad SP Bhat 2009 Semistability, finite-time stability, differential inclusions, and discontinuous dynamical systems having a continuum of equilibria IEEE Trans Automatic Control 54 10 2465 2470 10.1109/TAC.2009. 2029397
15. Q Hui WM Haddad SP Bhat 2010 Finite-time semistability, Filippov systems, and consensus protocols for nonlinear dynamical networks with switching topologies Nonlinear Anal Hybrid Syst 4 557 573 10.1016/j.nahs.2010.03.002
16. P Li J Cao Z Wang 2007 Robust impulsive synchronization of coupled delayed neural networks with uncertainties Physica A Stat Theor Phys 373 261 272 10.1016/j.physa.2006.05.029 (Pubitemid 44647697)
17. X Liu J Cao 2011 Local synchronization of one-to-one coupled neural networks with discontinuous activations Cogn Neurodyn 5 13 20 10.1007/s11571-010-9132-y
18. X Liu T Chen W Lu 2009 Consensus problem in directed networks of multi-agents via nonlinear protocols Phys Lett A 373 35 3122 3127 10.1016/j.physleta.2009.06.054 1:CAS:528:DC%2BD1MXptlWltbk%3D
19. W Lu T Chen 2003 New conditions on global stability of Cohen-Grossberg neural networks Neural Comput 15 5 1173 1189 12803961 10.1162/089976603765202703 (Pubitemid 37049804)
20. W Lu T Chen 2004 Synchronization of coupled connected neural networks with delays IEEE Trans Circuits Syst I Regul Pap 51 12 2491 2503 10.1109/TCSI.2004.838308 (Pubitemid 40009470)
21. W. Lu T Chen 2005 Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions Neural Netw 18 3 231 242 10.1016/j.neunet.2004.09.004 (Pubitemid 40719525)
22. J Lu DWC Ho 2010 Globally exponential synchronization and synchronizability for general dynamical networks IEEE Trans Syst Man Cybern Part B 40 2 350 361 10.1109/TSMCB.2009.2023509
23. R Olfati-Saber RM Murray 2004 Consensus problems in networks of agents with switching topology and time-delays IEEE Trans Automatic Control 49 9 1520 1533 10.1109/TAC.2004.834113
24. L Wang F Xiao 2010 Finite-time consensus problems for networks of dynamic agents IEEE Trans Automatic Control 55 4 950 955 10.1109/TAC.2010.2041610
25. CW Wu 2005 Synchronization in networks of nonlinear dynamical systems coupled via a directed graph Nonlinearity 18 3 1057 1064 10.1088/0951-7715/18/3/ 007 (Pubitemid 43025955)
26. W Wu T Chen 2008 Global synchronization criteria of linearly coupled neural network systems with time-varying coupling IEEE Trans Neural Netw 19 2 319 332 18269962 10.1109/TNN.2007.908639 1:STN:280:DC%2BD1c7ht12hsQ%3D%3D (Pubitemid 351359296)
27. CW Wu LO Chua 1995 Synchronization in an array of linearly coupled dynamical systems IEEE Trans Circuits Syst I 42 8 430 447 10.1109/81.404047
28. X Yang J Cao 2010 Finite-time stochastic synchronization of complex networks Appl Math Model 34 11 3631 3641 10.1016/j.apm.2010.03.012
29. W Yu J Cao W Lu 2010 Synchronization control of switched linearly coupled neural networks with delay Neurocomputing 73 858 866 10.1016/j.neucom.2009.10. 009
30. F Zou JA Nossek 1993 Bifurcation and chaos in cellular neural networks IEEE Trans Circuits Syst I Fundam Theory Appl 40 3 166 173 10.1109/81.222797