Pattern formation in the Brusselator system

Journal of Mathematical Analysis and Applications

Volumn 309, Issue 1, 2005, Pages 151-166

  Peng, Rui ^a   Wang, Mingxin ^a,b  

^a SOUTHEAST UNIVERSITY   (China)

^b JIANGSU NORMAL UNIVERSITY   (China)

Author keywords

A priori estimates; Bifurcation; Existence; Pattern formation; Steady states; The Brusselator system

Indexed keywords

EID: 22144487744     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.12.026     Document Type: Article

References (30)

1. K.J. Brown F.A. Davidson Global bifurcation in the Brusselator system Nonlinear Anal. 12 1995 1713-1725
2. T.K. Callahan E. Knobloch Pattern formation in three-dimensional reaction-diffusion systems Phys. D 132 1999 339-362
3. A. Casal J.C. Eilbeck J. López-Gómez Existence and uniqueness of coexistence states for a predator-prey model with diffusion Differential Integral Equations 7 1994 411-439
4. X.F. Chen, W.M. Ni, Y.W. Qi, M.X. Wang, A strongly coupled predator-prey system with non-monotonic functional response, preprint
5. W.Y. Chen R. Peng Stationary patterns created by cross-diffusion for the competitor-competitor-mutualist model J. Math. Anal. Appl. 291 2004 550-564
6. M.G. Crandall P. Rabinowitz Bifurcation from simple eigenvalue J. Funct. Anal. 8 1971 321-340
7. E.N. Dancer A counterexample of competing species equations Differential Integral Equations 9 1996 239-246
8. M. Delgado J. López-Gómez A. Suarez On the symbiotic Lotka-Volterra model with diffusion and transport effects J. Differential Equations 160 2000 175-262
9. Y.H. Du Y. Lou Some uniqueness and exact multiplicity results for a predator-prey model Trans. Amer. Math. Soc. 349 1997 2443-2475
10. Y.H. Du Y. Lou Qualitative behavior of positive solutions of a predator-prey model: Effects of saturation Proc. Roy. Soc. Edinburgh Sect. A 131 2001 321-349
11. B. Ermentrout Strips or spots? Nonlinear effects in bifurcation of reaction diffusion equation on the square Proc. Roy. Soc. London 434 1991 413-417
12. T. Erneux E. Reiss Brusselator isolas SIAM J. Appl. Math. 43 1983 1240-1246
13. D. Henry Geometric Theory of Semilinear Parabolic Equations third printing Lecture Notes in Math. vol. 840 1993 Springer-Verlag Berlin
14. Y. Kan-on Existence and instability of Neumann layer solutions for a 3-component Lotka-Volterra model with diffusion J. Math. Anal. Appl. 243 2000 357-372
15. Y. Kan-on M. Mimura Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics SIAM J. Math. Anal. 29 1998 1519-1536
16. Y. Lou S. Martinez W.M. Ni On 3 × 3 Lotka-Volterra competition systems with cross-diffusion Discrete Contin. Dynam. Systems 6 2000 175-190
17. Y. Lou W.M. Ni Diffusion, self-diffusion and cross-diffusion J. Differential Equations 131 1996 79-131
18. Y. Lou W.M. Ni Diffusion vs. cross-diffusion: An elliptic approach J. Differential Equations 154 1999 157-190
19. M. Mimura Y. Nishiura Pattern formation in coupled reaction-diffusion systems Japan J. Indust. Appl. Math. 12 1995 385-424
20. G. Nicolis Patterns of spatio-temporal organization in chemical and biochemical kinetics SIAM-AMS Proc. 8 1974 33-58
21. L. Nirenberg Topics in Nonlinear Functional Analysis 2001 Amer. Math. Soc. Providence, RI
22. I. Prigogene R. Lefever Symmetry breaking instabilities in dissipative systems II J. Chem. Phys. 48 1968 1665-1700
23. P.Y.H. Pang M.X. Wang Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion Proc. London Math. Soc. 88 2004 135-157
24. P.Y.H. Pang M.X. Wang Qualitative analysis of a ratio-dependent predator-prey system with diffusion Proc. Roy. Soc. Edinburgh Sect. A 133 2003 919-942
25. R. Peng M.X. Wang Positive steady-state solutions of the Noyes-Field model for Belousov-Zhabotinskii reaction Nonlinear Anal. 56 2004 451-464
26. P. Rabinowitz Some global results for nonlinear eigenvalue problems J. Funct. Anal. 7 1971 487-513
27. A. Turing The chemical basis of morphogenesis Philos. Trans. Roy. Soc. Ser. B 237 1952 37-72
28. M.X. Wang Non-constant positive steady-states of the Sel'kov model J. Differential Equations 190 2003 600-620
29. M.X. Wang, Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion, Phys. D, in press
30. J.H. Wu G.S.K. Wolkowicz A system of resource-based growth models with two resources in the unstirred chemostat J. Differential Equations 172 2001 300-332