Change in types of neuronal excitability via bifurcation control

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 2, 2008, Pages

  Xie, Yong ^a,b   Aihara, Kazuyuki ^b   Kang, Yan Mei ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; HOPF BIFURCATION; NEURONS; NONLINEAR CONTROL SYSTEMS; TWO DIMENSIONAL;

BIFURCATION CONTROL; BIFURCATION DYNAMICS; NEURONAL EXCITABILITY; PERIODIC SPIKING;

FEEDBACK CONTROL;

EID: 40849097601     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.021917     Document Type: Article

References (29)

1. E. M. Izhikevich, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127400000840 10, 1171 (2000).
2. J. Rinzel and G. B. Ermentrout, in Methods in Neuronal Modelling: From Synapses to Networks, edited by, C. Koch, and, I. Segev, (MIT, Cambridge, MA, 1998), pp. 251-291.
3. B. S. Gutkin and G. B. Ermentrout, Neural Comput. NEUCEB 0899-7667 10.1162/089976698300017331 10, 1047 (1998).
4. S. Tsuji, T. Ueta, H. Kawakami, H. Fujii, and K. Aihara, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 17, 985 (2007).
5. Y. Xie, J. X. Xu, Y. M. Kang, S. J. Hu, and Y. B. Duan, Commun. Nonlinear Sci. Numer. Simul. ZZZZZZ 1007-5704 10, 823 (2005).
6. E. M. Izhikevich, Neural Networks NNETEB 0893-6080 10.1016/S0893-6080(01) 00078-8 14, 883 (2001).
7. Y. Xie, J. X. Xu, and S. J. Hu, Chaos, Solitons Fractals CSFOEH 0960-0779 21, 177 (2004).
8. D. J. Schulz, J. Exp. Biol. JEBIAM 0022-0949 209, 4821 (2006).
9. J. F. Disterhoft and M. M. Oh, Aging Cell 6, 327 (2007).
10. H. Misonou, D. P. Mohapatra, and J. S. Trimmer, Neurotoxicology NRTXDN 0161-813X 26, 743 (2005).
11. R. W. Stackman, R. S. Hammond, E. Linardatos, A. Gerlach, J. Maylie, J. P. Adelman, and T. Tzounopoulos, J. Neurosci. JNRSDS 0270-6474 22, 10163 (2002).
12. G. Chen, J. L. Moiola, and H. O. Wang, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1016/S0218-1274(00)00036-0 10, 511 (2000).
13. H. O. Wang, D. Chen, and G. Chen, in Proceedings of the 1998 IEEE, International Conference on Control Applications, Trieste, Italy (IEEE Press, New York, 1998), pp. 858-862.
14. J. Wang, L. Q. Chen, and X. Y. Fei, Chaos, Solitons Fractals CSFOEH 0960-0779 33, 217 (2007).
15. H. C. Lee and E. H. Abed, in Proceedings of the American Control Conference, Boston, MA, 1991 (American Automatic Control Council, Green Valley, AZ, 1991), pp. 206-211.
16. A. Raman and C. D. Mote, Jr., Int. J. Non-Linear Mech. IJNMAG 0020-7462 10.1016/S0020-7462(00)00014-7 36, 261 (2001).
17. H. O. Wang, E. H. Abed, and A. M. A. Hamdan, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. ITCAEX 1057-7122 10.1109/81.285684 41, 294 (1994).
18. H. O. Wang and E. H. Abed, Automatica ATCAA9 0005-1098 10.1016/0005-1098(94)00146-A 31, 1213 (1995).
19. E. H. Abed and J. H. Fu, Syst. Control Lett. SCLEDC 0167-6911 10.1016/0167-6911(86)90095-2 7, 11 (1986).
20. E. H. Abed, H. O. Wang, and R. C. Chen, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)90062-0 70, 154 (1994).
21. D. W. Berns, J. L. Moiola, and G. Chen, Automatica ATCAA9 0005-1098 10.1016/S0005-1098(98)80010-1 34, 1567 (1998).
22. W. Kang, SIAM J. Control Optim. SJCODC 0363-0129 10.1137/ S0363012995290288 36, 193 (1998).
23. M. A. Hassouneh, H. C. Lee, and E. H. Abed, in Proceeding of the 2004 American Control Conference, Boston, MA (IEEE Press, New York, 2004), pp. 3950-3955.
24. G. L. Wen and D. L. Xu, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2005.01.058 337, 93 (2005).
25. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 5th ed. (Springer, New York, 1997), pp. 150-152.
26. D. S. Chen, H. O. Wang, and G. Chen, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. ITCAEX 1057-7122 10.1109/81.928149 48, 661 (2001).
27. W. M. Liu, J. Math. Anal. Appl. JMANAK 0022-247X 182, 250 (1994).
28. B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students (SIAM, Philadelphia, PA, 2002).
29. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Application of Hopf Bifurcation, London Mathematical Society Lecture Note Series, Vol. 41 (Cambridge University Press, Cambridge, England, 1981), pp. 86-91.