Interspecific influence on mobility and Turing instability

Bulletin of Mathematical Biology

Volumn 65, Issue 1, 2003, Pages 143-156

  Huang, Yunxin ^a,b   Diekmann, Odo ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

^b HUBEI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037270589     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1006/bulm.2002.0328     Document Type: Article

References (35)

1. Allen, J. C. (1975). Mathematical models of species interactions in time and space. Am. Nat. 109, 319-342.
2. Almirantis, Y. and S. Papageorgiou (1991). Cross-diffusion effects on chemical and biological pattern formation. J. Theor. Biol. 151, 289-311.
3. Amann, H. (1990). Dynamics of quasilinear parabolic equations II. Reaction-Diffusion Syst., Differ. Integral Equations 3, 13-75.
4. Amann, H. (1993). Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in Function Spaces, Differential Operators and Nonlinear Analysis, Teubnertexte Math. 133, H. Schmeisser and H. Triebel (Eds), Teubner: Stuttgart and Leipzig, pp. 9-126.
5. Amann, H. (1995). Linear and Quasilinear Parabolic Problems, Vol. 1, Abstract Linear Theory, Basel, Boston, Berlin: Birkhauser Verlag.
6. Aronson, D. G. (1985). The role of diffusion in mathematical population biology: skellam revisited, in Mathematics in Biology and Medicine, Lecture Notes in Biomathematics 57, V. Capasso (Ed.), pp. 2-6.
7. Bernstein, C. (1984). Prey and predator emigration responses in the acarine system Tetranychus urticae-Phytoseiulus persimilis. Oecologia 61, 134-142.
8. Capasso, V. and A. Di Liddo (1994). Asymptotic behaviour of reaction-diffusion systems in population and epidemic models-the role of cross-diffusion. J. Math. Biol. 32, 453-463.
9. Chattopadhyay, J. and P. K. Tapaswi (1993). Order and disorder in biological systems through negative cross-diffusion of mitotic inhibitor - a mathematical model. Math. Comput. Modelling 17, 105-112.
10. Chattopadhyay, J. and P. K. Tapaswi (1997). Effect of cross-diffusion on pattern formation - a nonlinear analysis. Math. Comput. Modelling 48, 1-12.
11. Crowley, P. H. (1981). Dispersal and stability of predator-prey interactions. Am. Nat. 118, 673-701.
12. Durrett, R. and S. Levin (1994). The importance of being discrete (and spatial). Theor. Pop. Biol. 46, 363-394.
13. Edelstein-Keshet, L. (1987). Mathematical Models in Biology, Birkhauser Mathematics Series, New York: McGraw-Hill Inc.
14. Farkas, M. (1997). Two ways of modeling cross diffusion. Nonlinear Anal. TMA 30, 1225-1233.
15. Grindrod, P. (1996). The Theory and Applications of Reaction-Diffusion Equations, Oxford: Clarendon Press.
16. Hastings, A. (1990). Spatial heterogeneity and ecological models. Ecology 71, 426-428.
17. Holmes, E. E., M. A. Lewis, J. E. Banks and R. R. Veit (1994). Partial differential equations in ecology: spatial interactions and population dynamics. Ecology 75, 17-29.
18. Huang, Y. and O. Diekmann (2001). Predator migration in response to prey density: what are the consequences? J. Math. Biol. 43, 561-581.
19. Jansen, V. A. A. and A. L. Lloyd (2000). Local stability analysis of spatially homogeneous solutions of multi-patch systems. J. Math. Biol. 41, 232-252.
20. Jorńe, J. (1974). The effect of ionic migration on oscillations and pattern formation in chemical systems. J. Theor. Biol. 43, 375-380.
21. Lou, Y. and W.-M. Ni (1996). Diffusion, self-diffusion and cross-diffusion. J. Differ. Equations 131, 79-131.
22. Marcus, M. and H. Minc (1964). A Survey of Matrix Theory and Matrix Inequalities, Boston: Allyn and Bacon Inc.
23. Murray, J. D. (1993). Mathematical Biology, Berlin, Heidelberg, New York: Spinger.
24. Ni, W.-M. (1998). Diffusion, cross-diffusion and their spike-layer steady states. Notices AMS 45, 9-18.
25. Okubo, A. (1980). Diffusion and Ecological Problems: Mathematical Models, Berlin: Springer.
26. Okubo, A. and S. Levin (2000). Diffusion and Ecological Problems: Modern Perspectives, 2nd edn, Berlin: Spinger.
27. Othmer, H. G. and L. E. Scriven (1971). Instability and dynamic patterns in cellular networks. J. Theor. Biol. 32, 507-537.
28. Pels, B. (2001). Evolutionary dynamics of dispersal in predatory mites, PhD thesis, Amsterdam University.
29. Plahte, E. (2001). Pattern formation in discrete cell lattices. J. Math. Biol. 43, 411-445.
30. Sabelis, M. W. (1981). Biological control of two-spotted spider mites using phytoseid predators. Part I: Modelling the Predator-prey Interactions at the Individual Level. Wageningen: Agric Res Rep Centre for Agricultural Publication and Documentation.
31. Segel, L. A. (1984). Taxes in cellular ecology, in Mathematical Ecology, Lecture Notes in Biomathematics 54, S. A. Levin (Ed.), pp. 407-424.
32. Segel, L. A. and J. L. Jackson (1972). Dissipative structure: an explanation and an ecological example. J. Theor. Biol. 35, 545-559.
33. Shigesada, N., K. Kawasaki and E. Teramota (1979). Spatial segregation of interacting species. J. Theor. Biol. 79, 83-99.
34. Takafuji, A. (1977). The effect of successful dispersal of a phytoseiid mite Phytoseiulus persimilis. Athias-Henriot (Acarina: phytoseiidae) on the persistence in the interactive system between the predator and its prey. Res. Popul. Ecol. 18, 210-222.
35. Turing, A. (1952). The chemical basis of morphogenesis. Phil. Trans. R. Soc. B 237, 37-72.