Collision of travelling waves in a reaction-diffusion system with global coupling effect

SIAM Journal on Applied Mathematics

Volumn 59, Issue 3, 1998, Pages 920-941

  Kawaguchi, Satoshi ^a   Mimura, Masayasu ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b HIROSHIMA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; ELECTROMAGNETIC WAVE PROPAGATION; ONE DIMENSIONAL; PERTURBATION TECHNIQUES; PROBLEM SOLVING; TWO DIMENSIONAL;

GLOBAL COUPLING EFFECT; REACTION DIFFUSION SYSTEM; TRAVELLING WAVES;

WAVE EQUATIONS;

EID: 0344806279     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/s003613999630664x     Document Type: Article

References (16)

1. U. MIDDYA, M.D. GRAHAM, D. Luss, AND M. SHEINTUCH, Pattern selection in controlled reaction-diffusion systems, J. Chem. Phys., 98 (1993), pp. 2823-2836.
2. C. RADEHAUS, H. WILLEBRAND, R. DOHMEN, F.-J. NIEDERNOSTHEID, G. BENGEL, AND H.-G. PURWINS. Spatially periodic patterns in a dc gas-discharge system, Phys. Rev. A, 45 (1992), pp. 2546-2557.
3. F.-J. NIEDERNOSTHEID, R. DOHMEN, H. WILLEBRAND, B.S. KERNER, AND H.-G. PURWINS, Transition from pulsating to rocking localized structures in nonlinear dissipative distributive media with global inhibition, Phys. D. 69 (1993). pp. 425-435.
4. K. KRISCHER AND A. MIKHAILOV, Bifurcation to traveling spots in reaction-diffusion systems, Phys. Rev. Lett., 73 (1994), pp. 3165-3168.
5. T. OHTA, M. MIMURA, AND R. KOBAYASHI, Higher dimensional localized patterns in excitable media, Phys. D, 34 (1989), pp. 115-144.
6. 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), pp. 220-230.
7. F.-J. NIEDERNOSTHEIDE, B.S. KERNER, AND H.-G. PURWINS, Spontaneous appearances of rocking localized current filaments in a nonequilibrium distributive system, Phys. Rev. B, 46 (1992), pp. 7559-7570.
8. 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), pp. 7426-7446.
9. G. VESER, F. MERTENS, A.S. MIKHAILOV, AND R. IMBIHL, Global coupling in the presence of defect: synchronization in an oscillatory surface reaction, Phys. Rev. Lett., 71 (1993), pp. 935-938.
10. U. MIDDYA, M. SHEINTUCH, M.D. GRAHAM, AND D. Luss, Patterns of temperature pulses on electrically heated catalytic ribbons, Phys. D, 63 (1993), pp. 393-409.
11. F. MERTENS, R. IMBIHL, AND A. MIKHAILOV, Breakdown of global coupling in oscillatory chemical reactions, J. Chem. Phys., 99 (1993), pp. 8668-8671.
12. Y. NISHIURA AND M. MIMURA, Layer oscillations in reaction-diffusion systems, SIAM. J. Appl. Math., 49 (1989), pp. 481-514.
13. M. SUZUKI, T. OHTA, M. MIMURA, AND H. SAKAGUCHI, Breathing and wiggling motions in three-species laterally inhibitory systems, Phys. Rev. E, 52 (1995), pp. 3645-3655.
14. P. DE KEPPER, V. CASTETS, E. DULOS, AND J. BOISSONADE, Turing-type chemical patterns in the chrolite-iodide-malonic acid reaction, Phys. D, 49 (1991), pp. 161-169.
15. M.D. GRAHAM, U. MIDDYA, AND D. Luss, Pulses and global bifurcations in a nonlocal reaction-diffusion system, Phys. Rev. E, 48 (1993), pp. 2917-2923.
16. L.M. PISMEN, Turing patterns and solitary structures under global control, J. Chem. Phys., 101 (1994), pp. 3135-3146.