Synchronization of chaotic neurons coupled with gap junction with time delays in external electrical stimulation

Chaos, Solitons and Fractals

Volumn 35, Issue 3, 2008, Pages 512-518

  Wang, Jiang ^a   Deng, Bin ^a   Fei, Xiangyang ^a  

^a TIANJIN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC FIELD EFFECTS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; SYNCHRONIZATION; TIME DELAY;

CHAOTIC NEURONS; COUPLING STRENGTH; GAP JUNCTION;

CHAOTIC SYSTEMS;

EID: 34548630334     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.05.056     Document Type: Article

References (25)

1. Bennett M.V.L., and Verselis V.K. Biophysics of gap junction. Seminars Cell Biol 3 (1992) 29-47
2. Baigent S., Stark J., and Warner A. Convergent dynamics of two cells coupled by a nonlinear gap junction. Nonlinear Anal 47 (2001) 257-268
3. Baigent S., Stark J., and Warner A. Modeling the effect of gap junction nonlinearities in systems of coupled cells. J Theor Biol 186 (1997) 223-239
4. Vogel R., and Robert W. The electrophysiology of gap junctions and gap junction channels and their mathematical modeling. Biol Cell 94 (2002) 501-510
5. Baigent S. Cells coupled by voltage-dependent gap junctions: the asymptotic dynamical limit. BioSystems 68 (2003) 213-222
6. Dermietzel R. Gap junction wiring: a 'new' principle in cell-cell communication in the nervous system. Brain Res Rev 26 (1998) 176-183
7. Pecora L.M., and Carroll T.L. Synchronization in chaotic systems. Phys Rev Lett 64 (1990) 821-824
8. Pecora L.M., and Carroll T.L. Driving systems with chaotic signal. Phys Rev A 44 (1991) 2374-2383
9. Chiu C., Lin W., and Peng C. Asymptotic synchronization in lattices of coupled nonlinear Lorenz equations. Int J Bifur Chaos 10 (2000) 2717-2728
10. Wang C., and Ge S.S. Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos, Solitons & Fractals 12 (2001) 1199-1206
11. Chua L.O., Itah M., Kosarev L., and Eckert K. Chaos synchronization in Chua's circuits. J Circ Syst Comput 3 (1993) 93-108
12. Agiza H.N., and Yassen M.T. Synchronization of Rossler and Chen chaotic dynamical systems using active control. Phys Lett A 278 (2001) 191-197
13. Wang J., Deng B., and Fei X. Chaotic synchronization of two coupled neurons via nonlinear control in external electrical stimulation. Chaos, Solitons & Fractals 27 (2006) 1272-1278
14. Hu G., Xiao J., and Zheng Z. Chaos control (2000), Shanghai Scientist and Technological Education Publishing House, China
15. Pikovsky A., Rosenblum M., and Kurths J. Synchronization: a universal concept in nonlinear sciences (2001), Cambridge University Press, New York
16. Mirollo R.E., and Strogatz S.H. Synchronization of pulse-coupled biological oscillators. SIAM J Appl Math 50 (1990) 1645-1662
17. Nischwitz A., and Gluknder H. Local lateral inhibition - a key to spike synchronization. Biol Cybernet 73 (1995) 389
18. Hale J.K., and Lunel S.M.V. Introduction to functional differential equations (1993), Springer-Verlag, New York
19. Jing X.J., Tan D.L., and Wang Y.C. An LMI approach to stability of systems with severe time-delay. IEEE Trans Automat Cont 49 7 (2004) 1192-1195
20. Hale J.K. Theory of functional differential equations (1977), Springer-verlag, New York
21. Li C., Wang H., and Liao X. Delay-dependent robust stability of uncertain fuzzy systems with time-varying delays. IEE Proc Control Theory Appl 151 4 (2004) 417-421
22. Jiang W., Bin D., and Tsang K.M. Chaotic synchronization of neurons coupled with gap junction under external electrical stimulation. Chaos, Solitons & Fractals 22 (2004) 469-476
23. Thompson C.J., Bardos D.C., Yang Y.S., and Joyner K.H. Nonlinear cable models for cells exposed to electric fields I. General theory and space-clamped solutions. Chaos, Solitons & Fractals 10 (1999) 1825-1842
24. Mori T., and Kokame H. Stability of over(x, ̇) (t) = Ax (t) + Bx (t - τ). IEEE Trans Automatic Cont 34 (1989) 460-461
25. Parks PC, Hahn V. Stability Theory, Prentice Hall International Series in Systems and Control Engineering 1992.