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Waves in a simple, excitable or oscillatory, reaction-diffusion model. (English) Zbl 0456.92025

MSC:
92Exx Chemistry
92B05 General biology and biomathematics
34C25 Periodic solutions to ordinary differential equations
35A25 Other special methods applied to PDEs
35K55 Nonlinear parabolic equations
35B35 Stability in context of PDEs
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[1] Fife, P. C., McLeod, J. B.: The approach of solutions of nonlinear diffusion equations to traveling front solutions. Arch. Rat. Mech. Anal. 65, 335-361 (1977) · Zbl 0361.35035 · doi:10.1007/BF00250432
[2] Greenberg, J. M., Hassard, B., Hastings, S.D.: Pattern formation and periodic structures in systems modeled by reaction-diffusing equations. Bull. AMS 84, 1296-1327 (1978) · Zbl 0424.35011 · doi:10.1090/S0002-9904-1978-14560-1
[3] Hastings, S. P.: A winding number principle for spatial patterns in some semi-discrete models of excitable media, preprint (1980)
[4] Kopell, N., Howard, L. N.: Plane wave solutions to reaction-diffusion equations. Stud. Appl. Math. 52, 291-328 (1973) · Zbl 0305.35081
[5] Kuramoto, Y., Yamada, T.: Pattern formation in oscillatory chemical reactions. Prog. Theor. Physics 56, 724-740 (1976) · doi:10.1143/PTP.56.724
[6] Rinzel, J.: Impulse propagation in excitable systems. In: (W. E. Stewart, W. H. Ray, C. C. Corley, eds.) Dynamics and modelling of reactive systems. New York: Academic Press 1980
[7] Winfree, A. T.: The geometry of biological time. New York-Heidelberg: Springer-Verlag 1979 · Zbl 0447.92001
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