Controlling chaos in space-clamped FitzHugh-Nagumo neuron by adaptive passive method

Nonlinear Analysis: Real World Applications

Volumn 11, Issue 3, 2010, Pages 1752-1759

  Wei, Du Qu ^a   Luo, Xiao Shu ^a   Zhang, Bo ^b   Qin, Ying Hua ^a  

^a GUANGXI NORMAL UNIVERSITY   (China)

^b SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Adaptive control; Chaos control; FitzHugh Nagumo neuron; Passive control

Indexed keywords

ADAPTIVE CONTROL; ADAPTIVE LAWS; CHAOS CONTROL; CONTROLLING CHAOS; EQUIVALENT SYSTEM; EXTERNAL CURRENTS; PASSIVE CONTROL; PASSIVE METHODS; PASSIVE SYSTEMS;

ADAPTIVE CONTROL SYSTEMS; CHAOS THEORY; COMPUTER SIMULATION; PASSIVE NETWORKS;

CONTROLLERS;

EID: 77950915879     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2009.03.029     Document Type: Article

References (22)

1. Xu X., Hu H.Y., and Wang H.L. Stability switches Hopf bifurcation and chaos of a neuron model with delay-dependent parameters. Phys. Lett. A 354 (2006) 126-136
2. Kon'no Y., Saito T., and Torikai H. Rich dynamics of pulse-coupled spiking neurons with a triangular base signal. Neural Netw. 18 (2005) 523-531
3. Liu Q., et al. Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation. Nonlinear Anal. RWA (2008) 10.1016/j.nonrwa.2008.04.025
4. Zhao L., Cáceres J.C.G., Damiance Jr. A.P.G., and Szu H. Chaotic dynamics for multi-value content addressable memory. Neurocomputing 69 (2006) 1628-1636
5. He G., Chen L., and Aihara K. Neurocomputing (2007) 10.1016/j.neucom.2007.09.005
6. Sabbagh H. Control of chaotic solutions of the Hindmarsh-Rose equations. Chaos Solitons Fractals 11 (2000) 1213-1218
7. Cortes J.M., Torres J.J., and Marro J. Control of neural chaos by synaptic noise. Biosystems 87 (2007) 186-190
8. Wang J., Zhang T., and Che Y. Chaos control and synchronization of two neurons exposed to ELF external electric field. Chaos Solitons Fractals 34 (2007) 839-850
9. Willems J.C. Dissipative dynamical systems part I: General theory. Arch. Ration. Mech. Anal. 45 (1972) 321-351
10. Byrnes C.I., Isidori A., and Willems J.C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear system. IEEE Trans. Automat. Control 36 (1991) 1228-1240
11. Lin W. Global robust stabilization of minimum-phase nonlinear systems with uncertainty. Automatica 33 (1997) 453-462
12. Espinosa-Pérez G., Maya-Ortiz P., Velasco-Villa M., and Sira-Ramírez H. Passivity-based control of switched reluctance motors with nonlinear magnetic circuits. IEEE Trans. Control Syst. Technol. 12 (2004) 439-448
13. Leyva R., Cid-Pastor A., Alonso C., and Queinnec I. Passivity-based integral control of a boost converter for large-signal stability. IEE Proc. Control Theory Appl. 153 (2006) 139-146
14. Wei D.Q., and Luo X.S. Passive adaptive control of chaos in synchronous reluctance motor. Chinese Phys. B 17 (2008) 92-97
15. Li Z., Chen G.R., and Shi S.J. Robust adaptive tracking control for a class of uncertain chaotic systems. Phys. Lett. A 310 (2003) 40-43
16. Zheng X., et al. Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts. Nonlinear Anal. (2008) 10.1016/j.na.2008.01.037
17. Fitzhugh R. Impulse and physiological states in models of nerve membrane. Biophys. J. 1 (1961) 445-466
18. Nagumo J.S., Arimoto S., and Yoshizawa S. An active pulse transmission line simulating nerve axon. Proc. IRE. 50 (1962) 2061-2071
19. Chou M.H., and Lin Y.T. Exotic dynamic behavior of the forced Fitz Hugh-Nagumo equations. Comput. Math. Appl. 32 (1996) 109-119
20. Gao Y. Chaos and bifurcation in the space-clamped FitzHugh-Nagumo system. Chaos Solitons Fractals 21 (2004) 943-956
21. Wen Y. Passive equivalence of chaos in Lorenz system. IEEE Trans. Circuits Syst. -I 46 (1999) 876-881
22. Hindmarsh J.L., and Rose R.M. A model of neuronal bursting using three coupled first order differential equations. Proc. Roy. Soc. London Ser. B 221 (1984) 87-102