Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system

Chaos, Solitons and Fractals

Volumn 18, Issue 2, 2003, Pages 259-266

  Abdusalam, H A ^a,b   Fahmy, E S ^a  

^a CAIRO UNIVERSITY   (Egypt)

^b KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; LYAPUNOV METHODS; VECTORS;

TELEGRAPH EQUATIONS;

CONTROL SYSTEM ANALYSIS;

EID: 0037545465     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(02)00648-3     Document Type: Article

References (19)

1. Shigesada N., Kawasaki K., Teramoto E. Spatial segregation of interacting species. J. Theoret. Biol. 79:1979;83.
2. McDougall T., Turner J.S. Influence of cross diffusion on finger double-diffusive convection. Nature. 299:1982;812.
3. Tapaswi P.K., Saha A.K. Pattern formation and morphogenesis: a reaction diffusion model. Bull. Math. Biol. 48:1986;213.
4. Alimirantis Y., Papageorgiou S. Cross diffusion effects on chemical and biological pattern formation. J. Theoret. Biol. 151:1991;289.
5. Chattopadhyay J., Tapaswi P.K., Mukherjee D. Formation of a regular dissipative structure: a bifurcation and nonlinear analysis. Biosystems. 26:1992;211.
6. Chattopadhyay J., Tapaswi P.K. Order and disorder in biological systems through negative cross-diffusion of mitotic inhibitor. Math. Comp. Model. 17:1993;105.
7. Chattopadhyay J., Tapaswi P.K. Morphogenetic prepattern during embryonic development - a nonlinear analysis. Appl. Math. Lett. 5:1992;19.
8. Tapaswi P.K., Chattopadhyay J. Turing structure during embryogenesis. Biosystems. 29:1993;25.
9. Kerner E.H. Further consideration on the statistical mechanics of biological associations. Bull. Math. Bioph. 21:1959;217.
10. Segel L.A., Jackson J.L. Dissipative structure: an explanation and an ecological example. J. Theoret. Biol. 37:1972;354.
11. Gurtin M.E. Some mathematical models for population dynamics that lead segregation. Quart. J. Appl. Math. 32:1974;1.
12. Chattopadhyay J., Chatterjee S. Cross diffusional effect in a Lotka-Volterra competitive system. Nonlinear Phenom. Complex Syst. 4(4):2001;364.
13. Murray J.D. Mathematical Biology. 1993;Springer-Verlag, New York.
14. Turing A.M. The chemical basis of morphogenesis. Philos. Trans. R. Soc. 237:1952;37.
15. Cattaneo G. Atti. Semi. Mat. Fis. Univ. Modena. 3:1948;83.
16. Ahmed E., Hassan S.Z. On diffusion and some biological economic systems. Z. Naturforsch. 55a:2000;669.
17. Ahmed E., Abdusalam H.A., Fahmy E.S. On telegraph coupled map lattice and its applications. Int. J. Mod. Phys. C. 12(10):2001;1527.
18. Ahmed E., Abdusalam H.A., Fahmy E.S. On telegraph reaction diffusion and coupled map lattice in some biological systems. Int. J. Mod. Phys. C. 12(5):2001;717.
19. Mckean H.P. Nagumo's equation. Adv. Math. 4:1970;209.