Periodic synchronization control of discontinuous delayed networks by using extended Filippov-framework

Neural Networks

Volumn 68, Issue , 2015, Pages 96-110

  Cai, Zuowei ^a   Huang, Lihong ^a,b   Guo, Zhenyuan ^b,c   Zhang, Lingling ^a   Wan, Xuting ^a  

^a HUNAN WOMEN S UNIVERSITY   (China)

^b HUNAN UNIVERSITY   (China)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Discontinuous neuron activations; Filippov framework; Functional differential inclusions; Neural networks; Periodic synchronization; Switching state feedback control

Indexed keywords

CHEMICAL ACTIVATION; DIFFERENTIAL EQUATIONS; FEEDBACK; FEEDBACK CONTROL; FIXED POINT ARITHMETIC; NEURONS; STATE FEEDBACK; SYNCHRONIZATION;

DELAYED NEURAL NETWORKS; DRIVE-RESPONSE NETWORKS; FILIPPOV; FUNCTIONAL DIFFERENTIAL EQUATIONS; FUNCTIONAL DIFFERENTIAL INCLUSIONS; GLOBAL EXPONENTIAL SYNCHRONIZATIONS; SYNCHRONIZATION CONTROL; SYNCHRONIZATION PROBLEM;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; CONCEPTUAL FRAMEWORK; DELAYED NEURAL NETWORK; FEEDBACK SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; NERVE CELL STIMULATION; NERVOUS SYSTEM PARAMETERS; NEUROTRANSMISSION; PERIODIC SYNCHRONIZATION; PERIODICITY; PRIORITY JOURNAL; SIGNAL PROCESSING; ALGORITHM; HUMAN; NERVE CELL; NERVE CELL NETWORK; PHYSIOLOGY; TIME;

ALGORITHMS; FEEDBACK; HUMANS; NERVE NET; NEURAL NETWORKS (COMPUTER); NEURONS; TIME FACTORS;

EID: 84930193887     PISSN: 08936080     EISSN: 18792782     Source Type: Journal    
DOI: 10.1016/j.neunet.2015.04.011     Document Type: Article

References (46)

1. Adhikari S.P., Yang C., Kim H., Chua L.O. Memristor bridge synapse-based neural network and its learning. IEEE Transactions on Neural Networks and Learning Systems 2012, 23(9):1426-1435.
2. Allegretto W., Papini D., Forti M. Common asymptotic behavior of solutions and almost periodicity for discontinuous, delayed, and impulsive neural networks. IEEE Transactions on Neural Networks 2010, 21(7):1110-1125.
3. Aubin J.P., Cellina A. Differential inclusions 1984, Springer-Verlag, Berlin.
4. Aubin J.P., Frankowska H. Set-valued analysis 1990, Birkhäuser, Boston, MA.
5. Berman A., Plemmons R.J. Nonnegative matrixes in mathematical science 1979, Academic Press, New York.
6. Cai Z.W., Huang L.H., Guo Z.Y., Chen X.Y. On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions. Neural Networks 2012, 33:97-113.
7. Chen G., Ueta T. Yet another chaotic attractor. International Journal of Bifurcation and Chaos 1999, 9(07):1465-1466.
8. Chua L.O. Memristor-the missing circuit element. IEEE Transactions on Circuit Theory 1971, CT-18:507-519. (2013). Memristor-based neural networks. Journal of Physics D, 46(9), 093001.
9. Clarke F.H. Optimization and nonsmooth analysis 1983, Wiley, New York.
10. Duan L., Huang L.H., Cai Z.W. Existence and stability of periodic solution for mixed time-varying delayed neural networks with discontinuous activations. Neurocomputing 2014, 123:255-265.
11. Filippov A.F. Differential equations with discontinuous right-hand side. Mathematics and its applications (Soviet series) 1988, Kluwer Academic, Boston.
12. Forti M., Grazzini M., Nistri P., Pancioni L. Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Physica D 2006, 214:88-89.
13. Forti M., Nistri P. Global convergence of neural networks with discontinuous neuron activations. IEEE Transactions on Circuits and Systems. I 2003, 50:1421-1435.
14. Forti M., Nistri P., Papini D. Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Transactions on Neural Networks 2005, 16(6):1449-1463.
15. Haddad G. Monotone viable trajectories for functional differential inclusions. Journal of Differential Equations 1981, 42(1):1-24.
16. Hale J.K. Theory of functional differential equations 1977, Springer-Verlag, New York.
17. Hong S.H., Wang L. Existence of solutions for integral inclusions. Journal of Mathematical Analysis and Applications 2006, 317:429-441.
18. Huang L.H., Cai Z.W., Zhang L.L., Duan L. Dynamical behaviors for discontinuous and delayed neural networks in the framework of Filippov differential inclusions. Neural Networks 2013, 48:180-194.
19. Huang L.H., Guo Z.Y. Global convergence of periodic solution of neural networks with discontinuous activation functions. Chaos, Solitons and Fractals 2009, 42:2351-2356.
20. Huang L.H., Guo Z.Y., Wang J.F. Theory and applications of differential equations with discontinuous right-hand sides 2011, Science Press, Beijing, (in Chinese).
21. Huang L.H., Wang J.F., Zhou X.N. Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations. Nonlinear Analysis. Real World Applications 2009, 10:1651-1661.
22. Huang L.H., Wu J.H. The role of threshold in preventing delay-induced oscillations of frustrated neural networks with McCulloch-Pitts nonlinearity. International Journal of Mathematics, Game Theory, and Algebra 2001, 11(6):71-100.
23. Lasota A., Opial Z. An application of the Kukutani-Ky Fan theorem in the theory of ordinary differential equations. Bulletin de l'Academie Polonaise des Sciences. Serie des Sciences Mathematiques, Astronomiques et Physiques 1965, 13:781-786.
24. Liu X.Y., Cao J.D. On periodic solutions of neural networks via differential inclusions. Neural Networks 2009, 22(4):329-334.
25. Liu X.Y., Cao J.D., Huang G. Complete periodic synchronization of delayed neural networks with discontinuous activations. International Journal of Bifurcation and Chaos 2010, 20(07):2151-2164.
26. Liu X.Y., Cao J.D., Yu W.W. Filippov systems and quasi-synchronization control for switched networks. Chaos 2012, 22(3). Article ID 033110.
27. Liu X.Y., Chen T.P., Cao J.D., Lu W.L. Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Networks 2011, 24:1013-1021.
28. Lu W., Chen T. Almost periodic dynamics of a class of delayed neural networks with discontinuous activations. Neural Computation 2008, 20(4):1065-1090.
29. O'Regan D. Integral inclusions of upper semi-continuous or lower semi-continuous type. Proceedings of the American Mathematical Society 1996, 124:2391-2399.
30. Papini D., Taddei V. Global exponential stability of the periodic solution of a delayed neural networks with discontinuous activations. Physics Letters A 2005, 343:117-128.
31. Qin S.T., Xue X.P., Wang P. Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations. Information Sciences 2013, 220(20):367-378.
32. Sprott J.C. A new class of chaotic circuit. Physics Letters A 2000, 266(1):19-23.
33. Suzuki K., Imai Y. Periodic chaos synchronization in slave subsystems using optical fiber ring resonators. Optical Communications 2004, 241:507-512.
34. Turkoglu D., Altun I. A fixed point theorem for multi-valued mappings and its applications to integral inclusions. Applied Mathematics Letters 2007, 20:563-570.
35. Wang K.N., Michel A.N. Stability analysis of differential inclusions in Banach space with application to nonlinear systems with time delays. IEEE Transactions on Circuits and Systems. I 1996, 43(8):617-626.
36. Wen S.P., Huang T.W., Zeng Z.G., Chen Y.R., Li P. Circuit design and exponential stabilization of memristive neural networks. Neural Networks 2015, 63:48-56.
37. Wen S.P., Zeng Z.G., Huang T.W., Li C.J. Passivity and passification of stochastic impulsive memristor-based piecewise linear system with mixed delays. International Journal of Robust and Nonlinear Control 2015, 25:610-624.
38. Wen S.P., Zeng Z.G., Huang T.W., Zhang Y.D. Exponential lag adaptive synchronization of memristive neural networks and applications in Pseudo-random generators. IEEE Transactions on Fuzzy Systems 2014, 22(6):1704-1713.
39. Wu H., Li R., Ding S., Zhang X., Yao R. Complete periodic adaptive anti-synchronization of memristor-based neural networks with mixed time-varying delays. Canadian Journal of Physics 2014, 92(11):1337-1349.
40. Wu H., Li R., Zhang X., Yao R. Adaptive finite-time complete periodic synchronization of memristive neural networks with time delays. Neural Processing Letters 2014, in press. 10.1007/s11063-014-9373-6.
41. Wu W., Zhang L., Ding S., Guo X., Wang L. Complete periodic synchronization of memristor-based neural networks with time-varying delays. Discrete Dynamics in Nature and Society 2013, 2013. Article ID 140153.
42. Yang X., Cao J. Exponential synchronization of delayed neural networks with discontinuous activations. IEEE Transactions on Circuits and Systems. I 2013, 60(9):2431-2439.
43. Zecca P., Zezza P.L. Nonlinear boundary value problems in Banach spaces for multivalued differential equations in noncompact intervals. Nonlinear Analysis 1979, 3:347-352.
44. Zhou M.Q. Theory of functions of real variable function 2001, Peking University Press, Beijing, (in Chinese).
45. Zhou J., Huang H.B., Qi G.X., Yang P., Xie X. Communication with spatial periodic chaos synchronization. Physics Letters A 2005, 335:191-196.
46. Zou W., Zhan M. Complete periodic synchronization in coupled systems. Chaos 2008, 18(4). Article ID 043115.