Synchronization of recurrent neural networks with mixed time-delays via output coupling with delayed feedback

Nonlinear Dynamics

Volumn 70, Issue 1, 2012, Pages 677-691

  Balasubramaniam, P ^a   Vembarasan, V ^a  

^a GANDHIGRAM RURAL UNIVERSITY   (India)

Author keywords

Linear matrix inequalities; Lyapunov Krasovskii functional; Neural networks; Synchronization; Time delays

Indexed keywords

ACTIVATION FUNCTIONS; BOUNDEDNESS; CONVEX COMBINATIONS; DELAY-DEPENDENT; DELAYED FEEDBACK; DIFFERENTIABILITY; DISCRETE AND DISTRIBUTED DELAYS; GENERAL DESCRIPTION; LINEAR MATRIX INEQUALITY APPROACH; LYAPUNOV-KRASOVSKII FUNCTIONALS; MASTER-SLAVE; NUMERICAL RESULTS; OUTPUT COUPLING; OUTPUT FEEDBACK CONTROLLER; SYNCHRONIZATION CONTROL; TIME-VARYING DELAY;

LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NEURAL NETWORKS; RECURRENT NEURAL NETWORKS; TIME DELAY;

SYNCHRONIZATION;

EID: 84867901430     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0487-y     Document Type: Article

References (51)

1. Pecora, L.M.; Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821-824 (1990)
2. Chen, G.; Dong, X.: From Chaos to Order. World Scientific, (1998)
3. 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, 239-252 (2011)
4. Akhavan, A.; Samsudin, A.; Akhshani, A.: A symmetric image encryption scheme based on combination of nonlinear chaotic maps. J. Franklin Inst. 348, 1797-1813 (2011)
5. Li, C.; Li, Y.: Fast and robust image segmentation by small-world neural oscillator networks. Cogn. Neurodyn. 5, 209-220 (2011)
6. Yoshida, H.; Kurata, S.; Li, Y.; Nara, S.: Chaotic neural network applied to two-dimensional motion control. Cogn. Neurodyn. 4, 69-80 (2010)
7. Arenas, A.; Díaz-Guilera, A.; Kurths, J.; Moreno, Y.; Zhou, C.: Synchronization in complex networks. Phys. Rep. 469, 93-153 (2008)
8. Civalleri, P.P.; Gilli, M: On stability of cellular neural networks. J. VLSI Signal Process. 23, 429-435 (1999)
9. Civalleri, P.P.; Gilli, M: On dissipative two-state quantum cells and cellular networks. Int. J. Circuit Theory Appl. 32, 79-90 (2004)
10. Gilli, M.: Strange attractors in delayed cellular neural networks. IEEE Trans. Circuits Syst. I 40, 849-853 (1993)
11. Li, X.: Existence and global exponential stability of periodic solution for delayed neural networks with impulsive and stochastic effects. Neurocomputing 73, 749-758 (2010)
12. Li, X.; Rakkiyappan, R.; Balasubramaniam, P.: Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J. Franklin Inst. 348, 135-155 (2011)
13. Balasubramaniam, P.; Vembarasan, V.; Rakkiyappan, R.: Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 16, 2109-2129 (2011)
14. Lu, H.: Chaotic attractors in delayed neural networks. Phys. Lett. A 298, 109-116 (2002)
15. Zou, F.; Nossek, J.A.: A chaotic attractor with cellular neural networks. IEEE Trans. Circuits Syst. I(38), 811-812 (1991)
16. Kwon, O.M.; Park, J.H.; Lee, S.M.; Won, S.C.: LMI optimization approach to observer-based controller design of uncertain time-delay systems via delayed feedback. J. Optim. Theory Appl. 128, 103-117 (2006)
17. Kwon, O.M.; Park, J.H.: Guaranteed cost control for uncertain large-scale systems with time-delays via delayed feedback. Chaos Solitons Fractals 27, 800-812 (2006)
18. Kwon, O.M.; Park, J.H.: On decentralized guaranteed cost control for uncertain large scale systems with delays in subsystem interconnection using delayed feedback. J. Optim. Theory Appl. 129, 391-414 (2006)
19. Zhu, Q.; Cao, J.: Stability of Markovian jump neural networks with impulse control and time varying delays. Nonlinear Anal.; Real World Appl. 13, 2259-2270 (2012)
20. Zhu, Q.; Cao, J.: Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays. IEEE Trans. Neural Netw. Learning Syst. 23, 467-479 (2012)
21. Zhu, Q.; Cao, J.: Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays. IEEE Trans. Syst. Man Cybern.; Part B, Cybern. 41, 341-353 (2011)
22. Zhu, Q.; Cao, J.: Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 21, 1314-1325 (2010)
23. Zhu, Q.; Li, X.; Yang, X.: Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays. Appl. Comput. Math. 217, 6078-6091 (2011)
24. Yu, W.; Chen, G.; Lü, J.: On pinning synchronization of complex dynamical networks. Automatica 45, 429-435 (2009)
25. Sun, W.; Wang, R.; Wang, W.; Cao, J.: Analyzing inner and outer synchronization between two coupled discrete-time networks with time delays. Cogn. Neurodyn. 4, 225-231 (2010)
26. Liu, X.; Cao, J.: Local synchronization of one-to-one coupled neural networks with discontinuous activations. Cogn. Neurodyn. 5, 13-20 (2011)
27. Zhu, Q.; Cao, J.: Adaptive synchronization of chaotic Cohen-Grossberg neural networks with mixed time delays. Nonlinear Dyn. 61, 517-534 (2010)
28. Tang, Y.; Qiu, R.; Fang, A.; Miao, Q.: Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays. Phys. Lett. A 372, 4425-4433 (2008)
29. Zhu, Q.; Cao, J.: Adaptive synchronization under almost every initial data for stochastic neural networks with time varying delays and distributed delays. Commun. Nonlinear Sci. Numer. Simul. 16, 2139-2159 (2011)
30. Zhu, Q.; Cao, J.: pth moment exponential synchronization for stochastic delayed Cohen-Grossberg neural networks with Markovian switching. Nonlinear Dyn. 67, 829-845 (2012)
31. Yang, Y.; Cao, J.: Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects. Physica A 386, 492-502 (2007)
32. He, W.; Qian, F.; Cao, J.; Han, Q.L.: Impulsive synchronization of two nonidentical chaotic systems with time-varying delay. Phys. Lett. A 375, 498-504 (2011)
33. Balasubramaniam, P.; Chandran, R.; Theesar, S.J.S.: Synchronization of chaotic nonlinear continuous neural networks with time-varying delay. Cogn. Neurodyn. 5, 361-371 (2011)
34. Cheng, C.-J.; Liao, T.-L.; Hwang, C.-C.: Exponential synchronization of a class of chaotic neural networks. Chaos Solitons Fractals 24, 197-206 (2005)
35. Cui, B.; Lou, X.: Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Solitons Fractals 39, 288-294 (2009)
36. Gan, Q.; Xu, R.; Kang, X.: Synchronization of chaotic neural networks with mixed time delays. Commun. Nonlinear Sci. Numer. Simul. 16, 966-974 (2011)
37. Gao, X.; Zhong, S.; Gao, F.: Exponential synchronization of neural networks with time-varying delays. Nonlinear Anal. 71, 2003-2011 (2009)
38. Huang, H.; Feng, G.: Synchronization of nonidentical chaotic neural networks with time delays. Neural Netw. 22, 869-874 (2009)
39. Li, T.; Fei, S.-M.; Zhang, K.-J.: Synchronization control of recurrent neural networks with distributed delays. Physica A 387, 982-996 (2008)
40. Li, T.; Fei, S.-M.; Zhu, Q.; Cong, S.: Exponential synchronization of chaotic neural networks with mixed delays. Neurocomputing 71, 3005-3019 (2008)
41. Li, T.; Song, A.-G.; Fei, S.-M.; Guo, Y.-Q.: Synchronization control of chaotic neural networks with time-varying and distributed delays. Nonlinear Anal. 71, 2372-2384 (2009)
42. Li, X.; Bohner, M.: Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback. Math. Comput. Model. 52, 643-653 (2010)
43. Li, X.; Ding, C.; Zhu, Q.: Synchronization of stochastic perturbed chaotic neural networks with mixed delays. J. Franklin Inst. 347, 1266-1280 (2010)
44. Li, X.; Fu, X.: Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations. Commun. Nonlinear Sci. Numer. Simul. 16, 885-894 (2011)
45. Song, Q.: Design of controller on synchronization of chaotic neural networks with mixed time-varying delays. Neurocomputing 72, 3288-3295 (2009)
46. Park, J.H.; Kwon, O.M.: Guaranteed cost control of time-delay chaotic systems. Chaos Solitons Fractals 27, 1011-1018 (2006)
47. Yu, W.; Cao, J.: Synchronization control of stochastic delayed neural networks. Physica A 373, 252-260 (2007)
48. Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia (1994)
49. Kwon, O.M.; Park, J.H.; Lee, S.M.: An improved delay-dependent criterion for asymptotic stability of uncertain dynamic systems with time-varying delays. J. Optim. Theory Appl. 145, 343-353 (2010)
50. Gu, K.; Kharitonov, L.; Chen, J.: Stability of Time-Delay Systems. Birkhäuser, Boston (2003)
51. Park, P.G.; Ko, J.W.; Jeong, C.: Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47, 235-238 (2011)