Dynamical phase transitions in periodically driven model neurons

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

Volumn 79, Issue 2, 2009, Pages

  Mirollo, Renato ^a  

^a BOSTON COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); NEURONS;

DISCONTINUOUS BIFURCATIONS; DYNAMICAL PHASE TRANSITIONS; DYNAMICAL STATE; FIRST ORDERS; INTEGRATE-AND-FIRE NEURONS; LIMIT CYCLES; PERIODIC CURRENTS; PERIODIC STIMULUS; RETURN MAPS; VARIABLE MODELS;

PHASE TRANSITIONS;

EID: 61549140395     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.021904     Document Type: Article

References (25)

1. B. W. Knight, J. Gen. Physiol. 59, 734 (1972). 10.1085/jgp.59.6.734
2. J. P. Keener, Trans. Am. Math. Soc. 261, 589 (1980). 10.2307/1998382
3. J. P. Keener, F. C. Hoppenstead, and J. Rinzel, SIAM J. Appl. Math. 41, 503 (1981). 10.1137/0141042
4. S. Coombes and P. C. Bressloff, Phys. Rev. E 60, 2086 (1999); 10.1103/PhysRevE.60.2086
5. S. Coombes, M. R. Owen, and G. D. Smith, Phys. Rev. E 64, 041914 (2001); 10.1103/PhysRevE.64.041914
6. C. Laing and S. Coombes, Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, 1433 (2004).
7. K. Pakdaman, Phys. Rev. E 63, 041907 (2001). 10.1103/PhysRevE.63.041907
8. P. C. Bressloff and S. Coombes, Phys. Rev. Lett. 80, 4815 (1998); 10.1103/PhysRevLett.80.4815
9. P. C. Bressloff and S. Coombes, Phys. Rev. Lett. 81, 2168 (1998); 10.1103/PhysRevLett.81.2168
10. P. C. Bressloff and S. Coombes, Phys. Rev. Lett. 81, 2384 (1998); 10.1103/PhysRevLett.81.2384
11. P. C. Bressloff and S. Coombes, SIAM J. Appl. Math. 60, 820 (2000); 10.1137/S0036139998339643
12. P. C. Bressloff, S. Coombes, and B. de Souza, Phys. Rev. Lett. 79, 2791 (1997). 10.1103/PhysRevLett.79.2791
13. J. Rubin and A. Bose, Physica D 221, 37 (2006); 10.1016/j.physd.2006.07. 012
14. J. Rubin and A. Bose, Network Comput. Neural Syst. 15, 133 (2004). 10.1088/0954-898X/15/2/004
15. P. C. Bressloff and S. Coombes, Physica D 126, 99 (1999); 10.1016/S0167-2789(98)00264-4
16. P. C. Bressloff and S. Coombes, Physica D 130, 232 (1999). 10.1016/S0167-2789(99)00013-5
17. P. H. E. Tiesinga, J. V. José, and T. J. Sejnowski, Phys. Rev. E 62, 8413 (2000); 10.1103/PhysRevE.62.8413
18. P. H. E. Tiesinga, Phys. Rev. E 65, 041913 (2002); 10.1103/PhysRevE.65. 041913
19. P. H. E. Tiesinga, J. M. Fellous, and T. J. Sejnowski, Neurocomputing 44, 195 (2002). 10.1016/S0925-2312(02)00390-9
20. T. Gedeon and M. Holzer, J. Math. Biol. 49, 577 (2004). 10.1007/s00285-004-0268-4
21. D. T. Kaplan, J. R. Clay, T. Manning, L. Glass, M. R. Guevara, and A. Shrier, Phys. Rev. Lett. 76, 4074 (1996). 10.1103/PhysRevLett.76.4074
22. R. L. Devaney, An Introduction to Chaotic Dynamical Systems (Addison Wesley, New York, 1989).
23. J. A. Connor and C. F. Stevens, J. Physiol. (London) 213, 21 (1971).
24. P. Dayan and L. F. Abbott, Theoretical Neuroscience (MIT, Cambridge, MA, 2001).
25. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, New York, 1992).