Hiroshima Mathematical Journal

Dynamics of travelling breathers arising in reaction-diffusion systems---ODE modelling approach

Masayasu Mimura, Masaharu Nagayama, Hideo Ikeda, and Tsutomu Ikeda
Source: Hiroshima Math. J. Volume 30, Number 2 (2000), 221-256.
First Page: Show Hide
Primary Subjects: 35K57
Secondary Subjects: 34C99, 35B35
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.hmj/1206124685
Mathematical Reviews number (MathSciNet): MR1777514
Zentralblatt MATH identifier: 1003.65116

References

[1] M. Bar, M. Hildebrand, M. Eiswirth, M. Falcke, H. Engel and M. Neufeld, Chemical turbulence and standing waves in a surface reaction model: The influence of global coupling and wave instabilities, Chaos 4(3), 1994, 499-508.
[2] E. Doedel, H. B. Keller and J. P. Kernevez, Numerical analysis and control of bifurcation problems (I) Bifurcation in finite dimensions, Int. J. Bifurcation and Chaos 1, 1991, 493-520.
Zentralblatt MATH: 0876.65032
Mathematical Reviews (MathSciNet): MR1159608
[3] H. Ikeda and T. Ikeda, Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems, J. Dynamics and Differential Equations 12, 2000, 117-167.
Zentralblatt MATH: 0949.34030
Mathematical Reviews (MathSciNet): MR1758291
[4] T. Ikeda, H. Ikeda and M. Mimura, Hopf bifurcation of travelling pulses in some bistable reaction-diffusion systems, to appear in Methods and Applications of Analysis.
Zentralblatt MATH: 0982.35049
[5] M. Mimura and M. Nagayama, Nonannihilation dynamics in an exothermic reaction-diffusion system with mono-stable excitability, Chaos 7 (4), 1997, 817-826.
Zentralblatt MATH: 0933.35094
Mathematical Reviews (MathSciNet): MR1604722
[6] M. Mimura, M. Nagayama and T. Ohta, Nonannihilation of travelling pulses in reaction-diffusion systems, to appear in Methods and Applications of Analysis.
Zentralblatt MATH: 0908.35064
[7] J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE 50, 1962, 2061-2070.
[8] T. Ohta, J. Kiyose and M. Mimura, Collision of propagating pulse in a reaction-diffusion system, J. Phys. Soc. Japan 66, 1997, 1551-1558.
Zentralblatt MATH: 0963.35510
[9] J. Pearson, Complex patterns in a simple system, Sciences 261, 1993, 189-192.
[10] V. Petrov, S. K. Scott and K. Showalter, Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion systems, Phil. Trans. Roy. Soc. Lond. A347, 1994, 631-642.
Zentralblatt MATH: 0867.35047
[11] J. J. Tyson and P. C. Fife, Target patterns in a realistic model of the Belousov-Zhabotinskii reaction, J. Chem. Phys. 73 (5), 1980, 2224-2237.
Mathematical Reviews (MathSciNet): MR583644
[12] X.-F. Chen, Generation and propagation of interfaces in reaction-diffusion systems, Trans. Amer. Math. Soc. 334, 1992, 877-913.
Zentralblatt MATH: 0785.35006
Mathematical Reviews (MathSciNet): MR1144013

2013 © Hiroshima University, Department of Mathematics

Hiroshima Mathematical Journal

Hiroshima Mathematical Journal