Synchronization of coupled FitzHugh-Nagumo systems via MIMO feedback linearization control

Chaos, Solitons and Fractals

Volumn 33, Issue 1, 2007, Pages 194-202

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

^a TIANJIN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; FEEDBACK CONTROL; LINEARIZATION; SYNCHRONIZATION;

ADAPTIVE STRATEGY; LINEARIZATION ALGORITHMS; MULTI-INPUT MULTI-OUTPUT (MIMO) SYSTEMS;

NONLINEAR SYSTEMS;

EID: 33846809290     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.01.037     Document Type: Article

References (35)

1. Pecora L.M., and Carroll T.L. Synchronization in chaotic systems. Phys Rev Lett 64 (1990) 821-824
2. Pecora L.M., and Carroll T.L. Driving systems with chaotic signal. Phys Rev A 44 (1991) 2374-2383
3. Uçar A., Lonngren K.E., and Bai E.-W. Synchronization of the coupled FitzHugh-Nagumo systems. Chaos, Solitons & Fractals 20 5 (2004) 1085-1090
4. Liu F., Ren Y., Shan X., and Qiu Z. A linear feedback synchronization theorem for a class of chaotic systems. Chaos, Solitons & Fractals 13 4 (2002) 723-730
5. Pikovsky A., Rosenblum M., and Kurths J. Synchronization: a universal concept in nonlinear sciences (2001), Cambridge University Press, New York
6. Zhang G.-J., and Xu J.-X. Stochastic resonance induced by novel random transitions of motion of FitzHugh-Nagumo neuron model. Chaos, Solitons & Fractals 23 4 (2005) 1439-1449
7. Gao Y. Chaos and bifurcation in the space-clamped FitzHugh-Nagumo system. Chaos, Solitons & Fractals 21 4 (2004) 943-956
8. Jing Z., Chang Y., and Guo B. Bifurcation and chaos in discrete FitzHugh-Nagumo system. Chaos, Solitons & Fractals 21 3 (2004) 701-720
9. Marquié P., Comte J.C., and Morfu S. Analog simulation of neural information propagation using an electrical FitzHugh-Nagumo lattice. Chaos, Solitons & Fractals 19 1 (2004) 27-30
10. Feki M. An adaptive chaos synchronization scheme applied to secure communication. Chaos, Solitons & Fractals 18 1 (2003) 141-148
11. Bazhenov M., Huerta R., Rabinovich M.I., and Sejnowski T. Cooperative behavior of a chain of synaptically coupled chaotic neurons. Physica D 116 (1998) 392
12. Collins J.J., and Stewart I. Nonlinear Sci 3 (1995) 349
13. Lü J., Zhou T., and Zhang S. Chaos synchronization between linearly coupled chaotic systems. Chaos, Solitons & Fractals 14 (2002) 529-541
14. Chiu C., Lin W., and Peng C. Asymptotic synchronization in lattices of coupled nonlinear Lorenz equations. Int J Bifur Chaos 10 (2000) 2717-2728
15. Yassen M.T. Feedback and adaptive synchronization of chaotic Lü system. Chaos, Solitons & Fractals 25 2 (2005) 379-386
16. Hu G., Xiao J., and Zheng Z. Chaos control (2000), Shanghai Scientist and Technological Education Publishing House, China
17. Rajasekar S., Murali K., and Lakshmanan M. Control of chaos by nonfeedback methods in a simple electronic circuit system and the FitzHugh-Nagumo equation. Chaos, Solitons & Fractals 8 9 (1997) 1545-1558
18. Zhang H., and Holden A.V. Chaotic meander of spiral waves in the FitzHugh-Nagumo system. Chaos, Solitons & Fractals 5 3-4 (1995) 661-670
19. 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 11 (1999) 1825-1842
20. Ott E., Grebogi C., and Yorke J.A. Controlling chaos. Phys Rev Lett 64 (1990) 1196-1199
21. Park J.H. Adaptive synchronization of a unified chaotic systems with an uncertain parameter. Int J Nonlinear Sci Numer Simul 6 (2005) 201-206
22. Yang X.S., and Chen G. Some observer-based criteria for discrete-time generalized chaos synchronization. Chaos, Solitons & Fractals 13 (2002) 1303-1308
23. Cao J., Li H.X., and Ho D.W.C. Synchronization criteria of Lur'e systems with time-delay feedback control. Chaos, Solitons & Fractals 23 (2005) 1285-1298
24. Deng B., Wang J., and Fei X. Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control. Chaos, Solutions & Fractals 29 1 (2006) 182-189
25. Bowong S., and Moukam Kakmeni F.M. Synchronization of uncertain chaotic systems via backstepping approach. Chaos, Solitons & Fractals 21 (2004) 999-1011
26. Ho M.C., and Hung Y.C. Synchronization two different systems by using generalized active control. Phys Lett A 301 (2002) 424-428
27. Fotsin H., and Bowong S. Adaptive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators. Chaos, Solitons & Fractals 27 3 (2006) 822-835
28. Yassen M.T. Controlling chaos and synchronization for new chaotic system using linear feedback control. Chaos, Solitons & Fractals 26 3 (2005) 913-920
29. Jiang G.-P., and Xing Zheng W. An LMI criterion for linear-state-feedback based chaos synchronization of a class of chaotic systems. Chaos, Solitons & Fractals 26 2 (2005) 437-443
30. Guo Lu J. Generating chaos via decentralized linear state feedback and a class of nonlinear functions. Chaos, Solitons & Fractals 25 2 (2005) 403-413
31. 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
32. 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, Solutions & Fractals 10 (1999) 1825-1842
33. Godbole D.N., and Sastry S.S. Approximate decoupling and asymptotic tracking for MIMO systems. IEEE Trans Automatic Control 40 (1995) 441-450
34. Femat R., and Solís-Perales G. On the chaos synchronization phenomena. Phys Lett A 262 (1999) 50
35. Femat R., Alvarez-Ramírez J., and Fernández-Anaya G. Adaptive synchronization of high-order chaotic systems: a feedback with low-order parameterizations. Physica D 139 (2000) 231