Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 255, Issue 1-2, 1999, Pages 49-57

  Coombes, S ^a  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

Circle map; Integrate and fire; Liapunov exponent

Indexed keywords

BIOLOGICAL OSCILLATORS; CIRCLE MAP; FIRING MECHANISM; INTEGRATE AND FIRES; LIAPUNOV EXPONENTS; LINEAR STABILITY; MODE-LOCKED;

DYNAMICAL SYSTEMS;

EID: 0001908316     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-9601(99)00172-3     Document Type: Article

References (19)

1. F. Rieke, D. Warland, R. de Ruyter van Steveninck, W. Bialek, Spikes, MIT Press, 1997.
2. L. Glass, M.C. Mackey. From Clocks to Chaos, Princeton University Press, 1988.
3. H.C. Tuckwell, Introduction to Theoretical Neurobiology: I, Cambridge University Press, 1988.
4. P.C. Bressloff, S. Coombes, Dynamics of strongly-coupled spiking neurons, To appear in Neural Computation, 1999.
5. P.C. Muller, Chaos, Solitons and Fractals 5 (1995) 1671.
6. J.J. Hopfield, Nature 376 (1995) 33.
7. L. Glass, M.C. Mackey, Journal of Mathematical Biology 7 (1979) 339.
8. L. Glass, J. Belair, Continuation of Arnold tongues in mathematical models of periodically forced biological oscillators, in: H.G. Othmer (Ed.) Nonlinear Oscillations in Biology and Chemistry, pages 232-243. Springer-Verlag, 1980.
9. R.S. Mackay, C. Tresser, Physica D 19 (1986) 206.
10. L. Glass, M.R. Guevara, A. Shrier, R. Perez, Physica D 7 (1983) 89.
11. T. Horita, H. Hata, H. Mori, Progress in Theoretical Physics 84 (1990) 558.
12. G.A. Petrillo, L. Glass, A theory for phase locking of respiration in cats to a mechanical ventilator, Americal Journal of Physiology 246 (1984) R311-R320.
13. S. Daan, D.G.M. Beersma, A.A. Borbely, Timing of human sleep: recovery process gated by a circadian pacemaker, Americal Journal of Physiology 246 (1984) R161-R178.
14. J. Belair, L. Glass, Physica D 16 (1985) 143.
15. R. Perez, L. Glass, Physics Letters A 90 (1982) 441.
16. M.R. Guevara, L. Glass, Journal of Mathematical Biology 14 (1982) 1.
17. L. Glass, M.R. Guevara, J. Belair, A. Shrier, Physical Review A 29 (1984) 1348.
18. J.P. Keener, L. Glass, Journal of Mathematical Biology 21 (1984) 175.
19. J.P. Keener, F.C. Hoppensteadt, J. Rinzel, SIAM Journal of Applied Maths 41 (1981) 816.