Stability of travelling fronts in a piecewise-linear reaction-diffusion system

Nonlinearity

Volumn 13, Issue 6, 2000, Pages 2063-2076

  Zemskov, E P ^a   Zykov, S V ^a   Kassner, K ^a   Muller S C ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034310984     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/13/6/309     Document Type: Article

References (38)

1. Kuramoto Y 1984 Chemical Oscillations, Waves and Turbulence (Berlin: Springer)
2. Kuramoto Y 1980 Prog. Theor. Phys. 63 1885
3. Meron E 1992 Phys. Rep. 218 1
4. Cross M C and Hohenberg P C 1993 Rev. Mod. Phys. 65 851
5. Hagberg A and Meron E 1993 Phys. Rev. E 48 705
6. Nishiura Y and Mimura M 1989 SIAM J. Appl. Math. 49 481
7. Kerner B S and Osipov V V 1989 Sov. Phys.-Usp. 32 101
8. Zykov V S, Mikhailov A S and Müller S C 1998 Phys. Rev. Lett. 81 2811
9. Markstein G H 1951 J. Aeronaut. Sci. 3 18
10. Zeldovich Ya B, Barenblatt GI, Librovich V B and Makhviladze G M 1985 Mathematical Theory of Combustion and Explosion (New York: Consultants Bureau)
11. Lee K J, McCormick W D, Quang Q and Swinney H L 1993 Science 261 192
12. Hagberg A and Meron E 1994 Chaos 4 477 Hagberg A and Meron E 1994 Nonlinearity 7 805
13. Hagberg A and Meron E 1994 Chaos 4 477 Hagberg A and Meron E 1994 Nonlinearity 7 805
14. Tyson J J and Fife P C 1980 J. Chem. Phys. 73 2224
15. Keener J P 1980 SIAM J. Appl. Math. 39 528
16. Keener J P and Tyson J J 1986 Physica D 21 307
17. FitzHugh R 1961 Biophys. J 1 445 Nagumo J, Arimoto S and Yoshizawa S 1962 Proc. IRE 50 2061
18. FitzHugh R 1961 Biophys. J 1 445 Nagumo J, Arimoto S and Yoshizawa S 1962 Proc. IRE 50 2061
19. McKean H P 1970 Adv. Math. 4 209
20. Rinzel J and Keller J B 1973 Biophys. J 13 1313
21. Ohta T, Mimura M and Kobayashi R 1989 Physica D 34 115
22. Koga S 1995 Physica D 84 148
23. Ito A and Ohta T 1992 Phys. Rev. A 45 8374
24. Schütz P, Bode M and Gafiichuk V V 1995 Phys. Rev. E 52 4465
25. Rinzel J and Terman D 1982 SIAM J. Appl. Math. 42 1111
26. Mikhailov A S and Krinsky V I 1983 Physica D 9 346
27. Schütz P, Bode M and Purwins H-G 1995 Physica D 82 382
28. Kessler D A, Ner Z and Sander L M 1998 Phys. Rev. E 58 107 Kessler D A, Ner Z and Sander L M 1998 Preprint patt-sol/9802001 (http://xxx.lanl.gov))
29. Kessler D A, Ner Z and Sander L M 1998 Phys. Rev. E 58 107 (Kessler D A, Ner Z and Sander L M 1998 Preprint patt-sol/9802001 (http://xxx.lanl.gov))
30. Mikhailov A S 1994 Foundations of Synergetics I. Distributed Active Systems (Berlin: Springer)
31. Ikeda H, Mimura M and Nishiura Y 1989 Nonlin. Anal. TMA 13 507
32. Bode M, Reuter A, Schmeling R and Purwins H-G 1994 Phys. Lett. A 185 70
33. Coullet P, Lega J, Houchmanzadeh B and Lajzerowicz J 1990 Phys. Rev. Lett. 65 1352
34. Hagberg A, Meron E, Rubinstein I and Zaltzman B 1997 Phys. Rev. E 55 4450
35. Kupferman R, Shochet O, Ben-Jacob E and Schuss Z 1992 Phys. Rev. B 46 16045
36. Scott S K and Showalter K 1995 Chemical Waves and Patterns ed R Kapral and K Showalter (Dordrecht: Kluwer) p 485 Showalter K 1995 Nonlin. Sci. Today 4 3
37. Scott S K and Showalter K 1995 Chemical Waves and Patterns ed R Kapral and K Showalter (Dordrecht: Kluwer) p 485 Showalter K 1995 Nonlin. Sci. Today 4 3
38. Bär M, Hagberg A, Meron E and Thiele U 2000 Phys. Rev. E 62 366