Synchronization in delayed Cohen-Grossberg neural networks with bounded external inputs

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 74, Issue 2, 2009, Pages 178-200

  Li, Chun Hsien ^a   Yang, Suh Yuh ^a  

^a NATIONAL CENTRAL UNIVERSITY   (Taiwan)

Author keywords

Cohen Grossberg neural networks; Discrete time delays; Distributed time delays; Exponential synchronization; Lyapunov functionals

Indexed keywords

CONTINUOUS TIME SYSTEMS; SYNCHRONIZATION; TELECOMMUNICATION NETWORKS; TIME DELAY; UNMANNED AERIAL VEHICLES (UAV);

COHEN-GROSSBERG NEURAL NETWORKS; DISCRETE TIME DELAYS; DISTRIBUTED TIME DELAYS; EXPONENTIAL SYNCHRONIZATION; LYAPUNOV FUNCTIONALS;

NEURAL NETWORKS;

EID: 63649089765     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxp003     Document Type: Article

References (31)

1. BELYKH, V. N., BELYKH, I. V. & HASLER, M.(2004) Connection graph stability method for synchronized coupled chaotic systems. Physica D 195, 159-187.
2. CHEN, G., ZHOU, J. & LIU, Z.(2004) Global synchronization of coupled delayed neural networks and applications to chaotic CNN models. Int. J. Bifurcat. Chaos, 14, 2229-2240.
3. CHEN, Y.(2006) Global asymptotic stability of delayed Cohen-Grossberg neural networks. IEEE Trans. Circuits Syst. I, 53, 351-357.
4. COHEN, M. A. & GROSSBERG, S.(1983) Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern., 13, 815-826.
5. DHAMALA, M., JIRSA, V. K. & DING, M.(2004a) Enhancement of neural synchrony by time delay. Phys. Rev. Lett., 92, 074104.
6. DHAMALA, M., JIRSA, V. K. & DING, M.(2004b) Transitions to synchrony in coupled bursting neurons. Phys. Rev. Lett., 92, 028101.
7. GOPALSAMY, K. & HE, X.-Z.(1994) Stability in asymmetric Hopfield nets with transmission delays. Physcia D, 76, 344-358.
8. HOPFIELD, J. J.(1984) Neurons with graded response have collective computational properties like two-state neurons. Proc. Natl. Acad. Sci. USA, 81, 3088-3092.
9. KOCAREV, L. & PARLITZ, U.(1995) General approach for chaotic synchronization with applications to communication. Phys. Rev. Lett. 74, 5028-5031.
10. LI, C. & CHEN, G.(2004) Synchronization in general complex dynamical networks with coupling delays. Physica A, 343, 263-278.
11. LI, C.-H. & YANG, S.-Y.(2007a) A further analysis on harmless delays in Cohen-Grossberg neural networks. Chaos Solitons Fractals 34, 646-653.
12. LI, C.-H. & YANG, S.-Y.(2007b) Exponential synchronization in drive-response systems of Hopfield-type neural networks with time delays. Int. J. Bifurcat. Chaos, 17, 4167-4176.
13. LIAO, X., LI, C. & WONG, K.-W.(2004) Criteria for exponential stability of Cohen-Grossberg neural networks. Neural Netw., 17 1401-1414.
14. LU, W. & CHEN, T.(2003) New condition on global stability of Cohen-Grossberg neural networks. Neural Comput., 15, 1173-1189.
15. MEDVEDEV, G. S. & KOPELL, N.(2001) Synchronization and transient dynamics in the chains of electrically coupled FitzHugh-Nagumo oscillators. SIAM J. Appl. Math., 61, 1762-1801.
16. MIROLLO, R. E. & STROGATZ, S. H.(1990) Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math., 50 1645-1662.
17. PECORA, L. M. & CARROLL, T. L.(1991a) Driving systems with chaotic signals. Phys. Rev. A, 44, 2374-2383.
18. PECORA, L. M. & CARROLL, T. L.(1991b) Synchronization in chaotic systems. Phys. Rev. Lett., 64, 821-824.
19. SHI, X. & LU, Q.-S.(2004) Complete synchronization of coupled Hindmarsh-Rose neurons with ring structure. Chin. Phys. Lett., 21, 1695-1698.
20. SHI, X. & LU, Q.-S.(2005) Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons. Chin. Phys., 14, 77-85.
21. SUN, J. & WAN, L.(2005) Global exponential stability and periodic solutions of Cohen-Grossberg neural networks with continuously distributed delays. Physica D, 208, 1-20.
22. TORAL, R., MASOLLER, C., MIRASSO, C. R., CISZAK, M. & CALVO, O. (2003) Characterization of the anticipated synchronization regime in the coupled FitzHugh-Nagumo model for neurons. Physica A, 325, 192-198.
23. UÇAR, A., LONNGREN, K. E. & BAI, E.-W.(2004) Synchronization of the coupled FitzHugh-Nagumo systems. Chaos Solitons Fractals, 20, 1085-1090.
24. VOSS, H. U.(2000) Anticipating chaotic synchronization. Phys. Rev. E, 61, 5115-5119.
25. VOSS, H. U.(2001) Dynamic long-term anticipation of chaotic states. Phys. Rev. Lett., 87, 014102.
26. WANG, L. & ZOU, X.(2002a) Exponential stability of Cohen-Grossberg neural networks. Neural Netw., 15, 415-422.
27. WANG, L. & ZOU, X.(2002b) Harmless delays in Cohen-Grossberg neural networks. Physica D, 170, 162-173.
28. WU, C. W.(2005) Synchronization in networks of nonlinear dynamical systems coupled via a directed graph. Nonlinearity, 18, 1057-1064.
29. WU, C. W. & CHUA, L. O.(1995) Synchronization in an array of linearly coupled dynamical systems. IEEE Trans. Circuits Syst. I, 42, 430-447.
30. YE, H., MICHEL, A. N. & WANG, K.(1995) Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. Phys. Rev. E 51, 2611-2618.
31. ZHOU, S., LIAO, X., YU, J. & WONG, K.-W.(2004) Chaos and its synchronization in two-neuron systems with discrete delays. Chaos Solitons Fractals, 21, 133-142.