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GLOBAL COUPLING EFFECTS ON A FREE BOUNDARY PROBLEM FOR THREE-COMPONENT REACTION-DIFFUSION SYSTEM
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 Title & Authors
GLOBAL COUPLING EFFECTS ON A FREE BOUNDARY PROBLEM FOR THREE-COMPONENT REACTION-DIFFUSION SYSTEM
Ham, Yoon-Mee;
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 Abstract
In this paper, we consider three-component reaction-diffusion system. With an integral condition and a global coupling, this system gives us an interesting free boundary problem. We shall examine the occurrence of a Hopf bifurcation and the stability of solutions as the global coupling constant varies. The main result is that a Hopf bifurcation occurs for global coupling and this motion is transferred to the stable motion for strong global coupling.
 Keywords
reaction-diffusion;global coupling;free boundary problem;Hopf bifurcation;
 Language
English
 Cited by
 References
1.
D. Battogtokh, M. Hildebrand, K. Krischer, and A.S. Mikhailov, Nucleation kinetics and global coupling in reaction-diffusion systems, Phys. Rep. 288 (1997), 435-456 crossref(new window)

2.
M. Bode and H. -G. Purwins, Pattern formation in reaction-diffusion systems- dissipative solitons in physical systems, Phys. D 86 (1995), no. 1-2, 53-63 crossref(new window)

3.
X. -F. Chen, Generation and propagation of interfaces in reaction-diffusion systems, Trans. Amer. Math. Soc. 334 (1992), no. 2, 877-913 crossref(new window)

4.
P. Fife, Dynamics of internal layers and diffusive interfaces, CBMS-NSF Regional Conference Series in Applied Mathematics Vol 53, SIAM, 1988

5.
P. Fife and J. Tyson, Target patterns in a realistic model of the Belousov- Zhabotinskii reaction, J. Chem. Phys. 73 (1980), no. 5, 2224-2237 crossref(new window)

6.
R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1 (1961), 445-466 crossref(new window)

7.
Y. M. Ham, Internal layer oscillations in FitzHugh-Nagumo equation, J. Comput. Appl. Math. 103 (1999), no. 2, 287-295 crossref(new window)

8.
Y. M. Ham, A Hopf bifurcation in a free boundary problem depending on the spatial average of an activator, International Journal of Bifurcation and Chaos 13 (2003), no. 10, 3135-3145 crossref(new window)

9.
Y. M. Lee, R. Schaaf, and R. Thompson, A Hopf bifurcation in a parabolic free boundary problem, J. Comput. Appl. Math. 52 (1994), no. 1-3, 305-324 crossref(new window)

10.
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol. 840, Springer, New York-Berlin, 1981

11.
S. Koga, Y. Kuramoto, Localized Patterns in Reaction-Diffusion Systems, Prog. Theor. Phys. 63 (1980), no. 1, 106-121 crossref(new window)

12.
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer, Berlin, 1984

13.
M. Meinhardt, Models of Biological Pattern Formation, Academic Press, London, 1982

14.
M. Meixner, P. Rodin, and E. Scholl, Global control of front propagation in gate- driven multilayered structures, Phys. Status Solidi (B) 204 (1997), no. 1, 493-496 crossref(new window)

15.
J. D. Murray, Mathematical Biology, Springer, Berlin, 1985

16.
J. Nagumo, S. Arimoto, and S. Yoshisawa, An active pulse transmission line simulating nerve axon, Proc. IRE. 50 (1962), 2061-2070

17.
Y. Nishiura and H. Fujii, Stability of singularly perturbed solutions to systems of reaction-diffusion equations, SIAM J. Math. Anal. 18 (1987), no. 6, 1726-1770 crossref(new window)

18.
Y. Nishiura and M. Mimura, Layer oscillations in reaction-diffusion systems, SIAM J. Appl. Math. 49 (1989), no. 2, 481-514 crossref(new window)

19.
T. Ohta, M. Mimura, and R. Kobayashi, Higher-dimensional localized patterns in excitable media, Phys. D 34 (1989), no. 1-2, 115-144 crossref(new window)

20.
C. Radehaus, R. Dohmen, H. Willebrand, and F. J. Niedernostheide, Model for current patterns in physical systems with two charge carriers, Phys. Rev. A. 42 (1990), 7426-7446 crossref(new window)

21.
K. Sakamoto, Spatial homogenization and internal layers in a reaction-diffusion system, Hiroshima Math. J. 30 (2000), no. 3, 377-402

22.
I. Schebesch and H. Engel, Self-Organization in Activator-Inhibitor Systems: Semiconductors, Gas Discharges and Chemical Active Media, Wissenschaft and Technik-Verlag, Berlin, 1996

23.
M. Suzuki, T. Ohta, M. Mimura, and H. Sakaguchi, Breathing and wiggling motions in three-species laterally inhibitory systems, Phys. Rev. E(3) 52 (1995), no. 4, part A, 3654-3655 crossref(new window)

24.
H. Willebrand, M. Or-Guil, M. Schilke, H. -G. Purwins, and Yu. A. Astrov, Experimental and numerical observation of quasiparticle like structures in a distributed dissipative system, Phys. Lett. A 177 (1993), no. 3, 220-224 crossref(new window)

25.
R. Woesler, P. Schutz, M. Bode, M. Or-Guil, and H. -G. Purwins, Oscillations of fronts and front pairs in two- and three-component reaction-diffusion systems, Phys. D 91 (1996), no. 4, 376-405 crossref(new window)