Avalanche-collapse mechanism: A model for excitability

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 6, Issue 10, 1996, Pages 1873-1881

  Plaza, F ^a   Velarde, M G ^a  

^a INSTITUTO PLURIDISCIPLINAR   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030268069     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812749600120X     Document Type: Article

References (19)

1. Antoranz, J. C., Gea, J. & Velarde, M. G. [1981] "Oscillatory phenomena and Q-switching in a model for a laser with saturable absorber," Phys. Rev. Lett. 47, 1895-1898.
2. 2 lasers with intracavity saturable absorbers," in Nonequilibrium Cooperative Phenomena in Physics and Related Fields, ed. Velarde, M. G. (Plenum Press, New York), pp. 117-135.
3. Busse, F. [1967] "Non-stationary finite amplitude convection," J. Fluid Mech. 28, 223-239.
4. Coullet, P. & Plaza, F. [1994] "Excitable spiral waves in nematic liquid crystals," Int. J. Bifurcation and Chaos 4(5), 1173-1182.
5. Dumortier, F. [1993] "Techniques in the theory of local bifurcations: blow-up, normal forms, nilpotent bifurcations, singular perturbations," in Bifurcations and Periodic orbits of Vector Fields, eds. Schlomiuk, D. (Kluwer Academic Press, Dordrecht), pp. 19-73.
6. FitzHugh, R. [1961] "Impulses and physiological states in theoretical models of nerve membrane," Biophys. J. 1, 445-466.
7. Frisch, T., Rica, S., Coullet, P. & Gilli, G. [1994] "Spiral waves in liquid crystals," Phys. Rev. Lett. 72, 1471-1473.
8. Garcia-Ybarra, P. L., Antoranz, J. C., Sankovitch, V. & Castillo, J. L. [1994] "Experimental evidence of self-excited relaxation oscillations leading to homoclinic behavior in spreading flames," Phys. Rev. E49, 5225-5229.
9. Hodgkin, A. L. & Huxley, A. F. [1952] "A quantitative description of membrane current and its application to conduction and excitation in nerves," J. Physiol. 117, 500-544.
10. Krinsky, V. I. [1984] "Autowaves: Results, problems, outlooks," in Self-Organization, Autowaves and Structures Far from Equilibrium, ed. Krinsky, V. I. (Springer-Verlag, Berlin), pp. 9-19.
11. Linde, H. [1984] "Time-dependent behavior and regularity of dissipative structures in interfacial dynamic instabilities," Faraday Discuss. Chem. Soc. 77, 181-200.
12. Meron, E. [1992] "Pattern formation in excitable media," Physics Rep. 218-1, 1-66.
13. Nagumo, J., Arimoto, S. & Yoshiwaza, S. [1962] "An active pulse transmission line simulating nerve axon," Proc. I.R.E. 50, 2061-2070.
14. Normand, C., Pomeau, Y. & Velarde, M. G. [1977] "Convective instability. A physicist's approach," Rev. Mod. Phys. 49, 581-624.
15. Noziéres, P. [1986] Lectures notes at Collège de France, unpublished.
16. Velarde, M. G. [1982] "Benard convection and laser with saturable absorber. Oscillations and chaos," in Evolution of Order and Chaos, in Physics, Chemistry and Biology, ed. Haken, H. (Springer-Verlag, Berlin), pp. 132-145.
17. Velarde, M. G. & Antoranz, J. C. [1986] "Intermittency and related phenomena in a simple model of a laser with saturable absorber," in Optical Instabilities, ed. Boyd, R. W., Raymer, M. G. & Narducci, L. M. (Cambridge University Press, Cambridge), pp. 132-145.
18. Weiss, C. O. & Vilaseca, R. [1991] Dynamics of Lasers (VCH Verlaggesellschaft, Weinheim), pp. 289-292.
19. Zaikin, A. N. & Zhabotinsky, A. M. [1970] "Concentration waves propagation in two-dimensional liquid-phase self-oscillating system," Nature 225, 535-537.