Transition fronts and localized structures in bistable reaction-diffusion equations

Physica D: Nonlinear Phenomena

Volumn 108, Issue 1-2, 1997, Pages 147-167

  Ermentrout, Bard ^a   Chen, Xinfu ^a   Chen, Zhixiong ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Bistability; Oscillations; Waves

Indexed keywords

EID: 0001505194     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)82011-8     Document Type: Article

References (17)

1. M.C. Cross and P.C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. (1993) 851-1112.
2. A.K. Dutt and S.C. Muller, Bistability in an uncatalyzed bromate oscillator in a continuously stirred tank reactor, J. Chem. Phys. 104 (1996) 583-586.
3. R.J. Field and M. Burger, eds., Oscillations and Traveling Waves in Chemical Systems (Wiley, New York, 1985).
4. P.C. Fife and J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rat. Mech. Anal. 65 (1977) 335-361.
5. D. Haim, G. Li, Q. Ouyang, W.D. McCormick, H.L. Swinney, A. Hagberg and E. Meron, Breathing spots in a reaction-diffusion system, preprint (1996).
6. J.L. Hindmarsh and R.M. Rose, A model of neuronal bursting using three coupled first order differential equations, Proc. Roy. Soc. London B 221 (1984) 87-102.
7. R. Kapral and K. Showalter, eds., Chemical waves and Patterns (Kluwer, Dordrecht, 1995).
8. G.A. Klassen and W.C. Troy, The stability of travelling wave front solutions of a reaction-diffusion system, SIAM J. Appl. Math. 36 (1981) 89-98.
9. R. Kobayashi, T. Ohta and Y. Hayase, Self-organized pulse generator, Physica D 84 (1995) 162-170.
10. N. Kopell and L.N. Howard, Plane wave solutions to reaction-diffusion equations, Stud. Appl. Math. 52 (1973) 291-328.
11. J.D. Murray, Mathematical Biology (Springer, New York, 1993).
12. J.E. Pearson, Complex patterns in a simple system, Science 261 (1993) 189-192.
13. J.A. Sherratt, The amplitude of periodic plane-waves depends on initial conditions in a variety of λ - ω systems, Nonlinearity 6 (1993) 1055-1066.
14. J.A. Sherratt, On the evolution of periodic plane-waves in reaction-diffusion systems of λ - ω type, SIAM J. Appl. Math. 54 (1994) 13.
15. J.A. Sherratt, Unstable wavetrains and chaotic wakes in reaction-diffusion systems of λ - ω type, Physica D 82 (1995) 165-179.
16. O. Thual and S. Fauve, Localized structures generated by subcritical instabilities, J. Phys. (Paris) 49 (1988) 1829-1833.
17. P.C. Fife, 1978.