Diffusion-driven instability in reaction-diffusion systems

Journal of Mathematical Analysis and Applications

Volumn 254, Issue 1, 2001, Pages 138-153

  Wang, Liancheng ^a   Li, Michael Y ^b  

^a GEORGIA SOUTHERN UNIVERSITY   (United States)

^b MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

Reaction diffusion systems; constant steady state; diffusion driven instability; stability; Lozinski measure; compound matrices

Indexed keywords

EID: 0035255650     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7220     Document Type: Article

References (20)

1. Casten R., Holland C. Stability properties of solutions to systems of reaction-diffusion equations. SIAM J. Appl. Math. 33:1977;353-364.
2. Casten R., Holland C. Instability results for reaction diffusion equations with Neumann boundary conditions. J. Differential Equations. 27:1978;266-273.
3. Coppel W. A. Stability and Asymptotic Behavior of Differential Equations. 1965;Heath, Boston.
4. Fiedler M. Additive compound matrices and inequality for eigenvalues of stochastic matrices. Czech Math. J. 99:1974;392-402.
5. Fiedler M., Praha V. P. On matrices with non-positive off-diagonal elements and positive principal minors. Czech Math. J. 12:1962;382-400.
6. Gantmacher F. R. The Theory of Matrices. 1959;Chelsea, New York.
7. Hale J. K. Ordinary Differential Equations. 1969;Wiley, New York.
8. Hillen T. A Turing model with correlated random walk. J. Math. Biol. 35:1996;49-72.
9. Iida M., Muramatsu T., Ninomiya H., Yanagida E. Diffusion-induced extinction of a superior species in competition systems. Japan J. Indust. Appl. Math. 15:1998;233-252.
10. Li M. Y., Wang L. A criterion for stability of matrices. J. Math. Anal. Appl. 225:1998;249-264.
11. Li M. Y., Graef J. R., Wang L., Karsai J. Global dynamics of an SEIR model with varying total population size. Math. Biosci. 160:1999;191-213.
12. Lou Y., Ni W.-M. Diffusion vs cross-diffusion: an elliptic approach. J. Differential Equations. 154:1999;157-190.
13. Lou Y., Ni W.-M. Diffusion, self-diffusion and cross-diffusion. J. Differential Equations. 131:1996;79-131.
14. Mizoguchi N., Ninomiya H., Yanagida E. Diffusion-induced blowup in a nonlinear parabolic system. J. Dynam. Differential Equations. 10:1998;619-638.
15. Muldowney J. S. Compound matrices and ordinary differential equations. Rocky Mountain J. Math. 20:1990;857-872.
16. Murray J. D. Mathematical Biology. 1993;Springer-Verlag, New York.
17. W.-M. Ni, Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc.45, 9-18.
18. Okubo A. Diffusion and Ecological Problems: Mathematical Models. 1980;Springer-Verlag, New York.
19. Smoller J. Shock Waves and Reaction-Diffusion Equations. 1994;Springer-Verlag, New York.
20. Turing A. The chemical basis of morphogenesis. Philos. Trans. Roy. Soc. London Ser. B. 237:1952;37-72.