Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach

Neural Networks

Volumn 57, Issue , 2014, Pages 79-93

  Chandrasekar, A ^a   Rakkiyappan, R ^a   Cao, Jinde ^b,c   Lakshmanan, S ^d  

^a BHARATHIAR UNIVERSITY   (India)

^b SOUTHEAST UNIVERSITY   (China)

^c KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^d UNITED ARAB EMIRATES UNIVERSITY   (United Arab Emirates)

Author keywords

Lyapunov Krasovskii functional; Memristor; Reciprocally convex approach; Synchronization; Time varying delays

Indexed keywords

INTEGRAL EQUATIONS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; MEMRISTORS; NONLINEAR CONTROL SYSTEMS; SYNCHRONIZATION; TIME DELAY; TIME VARYING CONTROL SYSTEMS;

ACTIVATION FUNCTIONS; CONVEX APPROACH; LYAPUNOV-KRASOVSKII FUNCTIONAL (LKF); LYAPUNOV-KRASOVSKII FUNCTIONALS; MEMRISTOR; OUTPUT FEEDBACK CONTROLLER; SYNCHRONIZATION CONTROL; TIME VARYING- DELAYS;

RECURRENT NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; CHAOTIC DYNAMICS; FEEDBACK SYSTEM; LINEAR MATRIX INEQUALITY TECHNIQUE; LINEAR SYSTEM; LYAPUNOV KRASOVSKII FUNCTIONAL METHOD; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL VARIABLE; MEMRISTOR BASED RECURRENT NEURAL NETWORK; PARTITION COEFFICIENT; PRIORITY JOURNAL; PROBLEM SOLVING; SECOND ORDER RECIPROCALLY CONVEX APPROACH; SIMULATION; TIME SERIES ANALYSIS; VALIDATION PROCESS; ALGORITHM; COMPUTER SIMULATION;

ALGORITHMS; COMPUTER SIMULATION; FEEDBACK; NEURAL NETWORKS (COMPUTER);

EID: 84904621851     PISSN: 08936080     EISSN: 18792782     Source Type: Journal    
DOI: 10.1016/j.neunet.2014.06.001     Document Type: Article

References (52)

1. Balasubramaniam P., Chandran R., Theesar S.J.S. Synchronization of chaotic nonlinear continuous neural networks with time-varying delay. Cognitive Neurodynamics 2011, 5:361-371.
2. Bao G., Zeng Z.G. Multistability of periodic delayed recurrent neural network with memristors. Neural Computing and Applications 2013, 23:1963-1967.
3. Boyd S., Ghaoui L.E., Feron E., Balakrishnan V. Linear matrix inequalities in system and control theory 1994, SIAM, Philadelphia, PA.
4. Cao J., Alofi A.S., Al-Mazrooei A., Elaiw A. Synchronization of switched interval networks and applications to chaotic neural networks. Abstract and Applied Analysis 2013, Art. no. 940573, 11 pages.
5. Cao J., Chen G., Li P. Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 2008, 38:488-498.
6. Cao J., Li L. Cluster synchronization in an array of hybrid coupled neural networks with delay. Neural Networks 2009, 22:335-342.
7. Cao J., Wan Y. Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Networks 2014, 53:165-172.
8. Cao J., Wang Z., Sun Y. Synchronization in an array of linearly stochastically coupled networks with time delays. Physica A 2007, 385:718-728.
9. Carroll T.L., Pecora L.M. Synchronization chaotic circuits. IEEE Transactions On Circuits and Systems 1991, 38:453-456.
10. Chen J., Zeng Z., Jiang P. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Networks 2014, 51:1-8.
11. Cheng C.J., Liao T.L., Hwang C.C. Exponential synchronization of a class of chaotic neural networks. Chaos, Solitons and Fractals 2005, 24:197-206.
12. Chua L. Memristor-the missing circuit element. IEEE Transactions on Circuit Theory 1971, 18:507-519.
13. Corinto F., Ascoli A., Gilli M. Nonlinear dynamics of memristor oscillators. IEEE Transactions on Circuits and Systems I: Regular Papers 2011, 58:1323-1336.
14. Gan Q., Xu R., Kang X. Synchronization of chaotic neural networks with mixed time delays. Communications in Nonlinear Science and Numerical Simulation 2011, 16:966-974.
15. Gao H., Chen T., Lam J. A new delay system approach to network-based control. Automatica 2008, 44:39-52.
16. Gao X., Zhong S., Gao F. Exponential synchronization of neural networks with time-varying delays. Nonlinear Analysis: Theory, Methods & Applications 2009, 71:2003-2011.
17. Gu K., Kharitonov V.L., Chen J. Stability of time-delay systems 2003, Birkhauser, Basel.
18. Huang H., Feng G., Cao J. Robust state estimation for uncertain neural networks with time-varying delay. IEEE Transactions on Neural Networks 2008, 19:1329-1339.
19. Itoh M., Chua L.O. Memristor oscillators. International Journal of Bifurcation and Chaos 2008, 18:3183-3206.
20. Lam J., Gao H., Wang C. Stability analysis for continuous systems with two additive time-varying delay components. Systems & Control Letters 2007, 56:16-24.
21. Lee W.I., Park P. Second-order reciprocally convex approach to stability of systems with interval time-varying delays. Applied Mathematics and Computation 2014, 229:245-253.
22. Li X., Bohner M. Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback. Mathematical and Computer Modelling 2010, 52:643-653.
23. Li X., Ding C., Zhu Q. Synchronization of stochastic perturbed chaotic neural networks with mixed delays. Journal of the Franklin Institute 2010, 347:1266-1280.
24. Li T., Fei S.M., Zhu Q., Cong S. Exponential synchronization of chaotic neural networks with mixed delays. Neurocomputing 2008, 71:3005-3019.
25. Liao T.L, Tsai S.H. Adaptive synchronization of chaotic systems and its application to secure communications. Chaos, Solitons and Fractals 2001, 11:1387-1396.
26. Liu M.Q. Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach. Neural Networks 2009, 22:949-957.
27. Liu Y., Hu L.-S., Shi P. A novel approach on stabilization for linear systems with time-varying input delay. Applied Mathematics and Computation 2012, 218:5937-5947.
28. Liu J., Zhang J. Note on stability of discrete-time time-varying delay systems. IET Control Theory & Applications 2012, 6:335-339.
29. Pan L., Zhou W., Fang J. On dynamics analysis of a novel three-scroll chaotic attractor. Journal of the Franklin Institute 2010, 347:508-522.
30. Park P., Ko J.W., Jeong C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica 2011, 47:235-238.
31. Park J.H., Kwon O.M. Guaranteed cost control of time delay chaotic systems. Chaos, Solitons and Fractals 2006, 27:1011-1018.
32. Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Physical Review Letters 1990, 64:821-824.
33. Perez-Munuzuri V., Perez-Villar V., Chua L.O. Autowaves for image processing on a two-dimensional CNN array of excitable nonlinear circuits: flat and wrinkled labyrinths. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 1993, 40:174-181.
34. Pershin Y.V., Di Ventra M. Experimental demonstration of associative memory with memristive neural networks. Neural Networks 2010, 23:881-886.
35. Shao H., Han Q. New delay-dependent stability criteria for neural networks with two additive time-varying delay components. IEEE transactions on Neural Networks 2011, 22:812-818.
36. Song Q. Design of controller on synchronization of chaotic neural networks with mixed time-varying delays. Neurocomputing 2009, 72:3288-3295.
37. Strukov D.B., Snider G.S., Stewart G.R., Williams R.S. The missing memristor found. Nature 2008, 453:80-83.
38. Sun W., Wang R., Wang W., Cao J. Analyzing inner and outer synchronization between two coupled discrete-time networks with time delays. Cognitive Neurodynamics 2010, 4:225-231.
39. Ventra M.D., Pershin Y.V., Chua L.O. Circuit elements with memory: memristors, memcapacitors, and meminductors. Proceedings of the IEEE 2009, 97:1717-1724.
40. Wang Z., Liu Y., Liu X. Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Transactions on Automatic Control 2010, 55:1656-1662.
41. Wang Y., Wang Z., Liang J. Global synchronization for delayed complex networks with randomly occurred nonlinearities and multiple stochastic disturbances. Journal of Physics A: Mathematical and Theoretical 2009, 42:135101.
42. Wang Y., Wang Z., Liang J. On robust stability of stochastic genetic regulatory networks with time-delays: a delay fractioning approach. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 2010, 40:729-740.
43. Wang Z., Wang Y., Liu Y. Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time-delays. IEEE Transactions on Neural Networks 2010, 21:11-25.
44. Wu A.L., Zeng Z.G. Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays. Neural Networks 2012, 36:1-10.
45. Wu A.L., Zeng Z.G. Exponential stabilization of memristive neural networks with time delays. IEEE Transactions on Neural Networks and Learning Systems 2012, 23:1919-1929.
46. Wu A.L., Zeng Z.G., Zhu X.S., Zhang J. Exponential synchronization of memristor-based recurrent neural networks with time delays. Neurocomputing 2011, 74:3043-3050.
47. Yang X., Cao J., Yu W. Exponential synchronization of memristive Cohen-Grossberg neural networks with mixed delays. Cognitive Neurodynamics 2014, 8:239-249.
48. Yu W., Cao J. Synchronization control of stochastic delayed neural networks. Physica A 2007, 373:252-260.
49. Zhang G.D., Shen Y., Sun J.W. Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays. Neurocomputing 2012, 97:149-154.
50. Zhang G.D., Shen Y., Wang L.M. Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays. Neural Networks 2013, 46:1-8.
51. Zhao Y., Gao H., Mou S. Asymptotic stability analysis of neural networks with successive time delay components. Neurocomputing 2008, 71:2848-2856.
52. Zhu Q., Cao J. pth moment exponential synchronization for stochastic delayed Cohen-Grossberg neural networks with Markovian switching. Nonlinear Dynamics 2012, 67:829-845.