Pattern formation in consumer-finite resource reaction-diffusion systems

Publications of the Research Institute for Mathematical Sciences

Volumn 40, Issue 4, 2004, Pages 1413-1431

  Mimura, Masayasu ^a  

^a MEIJI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18444380269     PISSN: 00345318     EISSN: 16634926     Source Type: Journal    
DOI: 10.2977/prims/1145475451     Document Type: Article

References (16)

1. Turing, A., The basis of morphogenesis, Phil. Trans. Royal Soc. Lond, B237 (1952), 37-72.
2. Hodgkin, A. L. and Huxley, A. F., A qualitative description of membrane current and its application to conductor and excitation in nerve, J. Physiology, 117 (1952), 500-544.
3. FitzHugh, R., Impulses and physiological states in theoretical models of nerve membrane, Biophysical J., 9 (1961), 445-466.
4. Casten, R. G. and Holland, C. J., Instability results for reaction-diffusion equations with Neumann boundary conditions, J. Differential Equations, 27 (1978), 266-273.
5. Ikeda, H., Mimura, M. and Nishiura, Y., Global bifurcation phenomena of traveling wave solutions for some bistable reaction-diffusion systems, Nonlinear Anal., 13 (1989), 507-526.
6. Nishiura, Y., Mimura, M., Ikeda, H. and Fujii, H., Singular limit analysis of stability of travelling wave solutions in bistable reaction-diffusion systems, SIAM J. Math. Anal., 21 (1990), 85-122.
7. Kermack, W. O. and McKendrick, A. G., A construction to the mathematical theory of epidemics, Part I, Proc. Royal Soc. Lond. Ser. A, 115 (1927), 700-721.
8. Grey, P. and Scott, S. K., Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Isolas and other forms of multistability, Chem. Eng., 9 (1996), 761-778.
9. Mimura, M. and Nagayama, M., Non-annihilation dynamics in an exothermic reaction-diffusion system with mono-stable excitability, CHAOS, 7 (1997), 817-826.
10. Masuda, K., On the global existence and asymptotic behavior of solutions of reaction-diffusion equations, Hokkaido Math. J., 12 (1983), 360-370.
11. Hoshino, H., On the convergence properties of global solutions for some reaction-diffusion systems under Neumann Boundary conditions, Diff. Integral Eqs., 9 (1996), 761-778.
12. Matsushita, M. et al., Formation of colony patterns by a bacterial cell population, Physica A, 274 (1999), 190-199.
13. Wakita, J. et al., Experimental investigation on the validity of population dynamics approach to bacterial colony formation, J. Phys. Soc. Japan, 63 (1994), 1205-1211.
14. Mimura, M., Sakaguchi, H. and Matsushita, M., Reaction-diffusion modeling of bacterial colony patterns, Phys. A, 282 (2000), 283-303.
15. Feiresl, E., Hilhorst, D., Mimura, M. and Weidenfeld, R., On nonlinear diffusion system with resource-consumer interaction, Hiroshima Math. J., 33 (2003), 253-295.
16. Matsuyama, T. and Matsushita, M., Population morphogenesis by cooperative bacteria, FORMA, 16 (2001), 307-326.