Continuum of weakly coupled oscillatory McKean neurons

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

Volumn 67, Issue 5 1, 2003, Pages

  Denman Johnson, M ^a   Coombes, S ^a  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CELLS; CONTINUUM MECHANICS; FOURIER TRANSFORMS; FUNCTIONS; MATHEMATICAL MODELS; NUMERICAL METHODS;

COUPLED OSCILLATOR THEORY; MCKEAN NEURONS; TRAVELING WAVE PHASE LOCKED SOLUTIONS;

NEUROPHYSIOLOGY;

EID: 42749102167     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. A.L. Hodgkin and A.F. Huxley, J. Physiol. (London) 116, 449 (1952).
2. D. Somers and N. Kopell, Biol. Cybern. 68, 393 (1993).
3. D. Terman and D. Wang, Physica D 81, 148 (1995).
4. E.M. Izhikevich, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 60, 1789 (2000).
5. J. Rubin and D. Terman, Neural Comput. 12, 597 (2000).
6. G.B. Ermentrout and N. Kopell, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 15, 215 (1984).
7. G.B. Ermentrout and N. Kopell, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 50, 125 (1990).
8. G.B. Ermentrout and N. Kopell, pulse interactions and averaging in systems of coupled neural oscillators, J. Math. Biol. 29, 195 (1991).
9. S. Coombes, Physica D 160, 173 (2001).
10. S. M. Crook, Ph.D. thesis, University of Maryland, 1996 (unpublished).
11. S.M. Crook, G.B. Ermentrout, M.C. Vanier, and J.M. Bower, J. Comput. Neurosci. 4, 161 (1997).
12. S.M. Crook, G.B. Ermentrout, and J.M. Bower, J. Comput. Neurosci. 5, 315 (1998).
13. P.C. Bressloff and S. Coombes, Int. J. Mod. Phys. B 11, 2343 (1997).
14. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, 1983).
15. B. Ermentrout, Neural Comput. 8, 979 (1996).
16. B. Ermentrout, SIAM, 2002. XPP software available from http://www.math.pitt.edu/~bard/xpp/xpp.html
17. N. Fenichel, Indiana Univ. Math. J. 21, 193 (1971).