Activator-inhibitor system with delay and pattern formation

Mathematical and Computer Modelling

Volumn 42, Issue 1-2, 2005, Pages 123-131

  Piotrowska, M J ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Equilibrium state; Morphogenesis; Pattern formation; Reaction diffusion equation; Stability; Turing instability

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PATTERN RECOGNITION; STABILITY;

EQUILIBRIUM STATE; MORPHOGENESIS; PATTERN FORMATION; REACTION-DIFFUSION EQUATION; TURING INSTABILITY;

NONLINEAR NETWORK ANALYSIS;

EID: 26844468477     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2004.05.010     Document Type: Article

References (16)

1. J.D. Murray Mathematical Biology 1989 Springer
2. F. Filbert, P. Laurencot, and B. Perthame Derivation of hyperbolic models for chemosensitive movement Int. Rep. ENS Paris, DMA 03-21 2003
3. K.P. Hadeler, T. Hillen and F. Lutscher, The Langevin Kramers approach to biological modelling, Math. Mod. Meth. Appl. Sci. (to appear).
4. A.M. Turing The chemical basis of morphogenesis Phil. Trans. Roy. Soc. London B237 1952 37 72
5. D. Thomas Artificial Enzyme Membranes, Transport, Memory, and Oscillatory Phenomena 1975 Springer Berlin
6. S.R. Choudhury, and C. Fosser Turing bifurcation in nonlinear competition models with delay Quarterly App. Math. LIV 1 1996 33 61
7. D. Henry Geometric Theory of Semilinear Parabolic Equations 1981 Springer-Verlag
8. J.-P. Kernevez Enzyme Mathematics 1980 North-Holland Publishing Company
9. J. Hale Theory of Functional Differential Equations 1977 Springer-Verlag Amsterdam
10. M. Bodnar The nonnegativity of solutions of delay differential equation Appl. Math. Lett. 13 6 2000 91 95
11. L.C. Evans Partial Differential Equations 1998 American Mathematical Society
12. Y. Kunag Delay Differential Equations with Application in Population Dynamics 1993 Academic Press Providence, RI
13. U. Foryś Biological delay systems and Mikhailov criterion of stability J. Biol. Sys. 12 1 2004 1 16
14. K. Cook, and Z. Grossman Discrete delay, distributed delay and stability switches J. Math. Anal. Appl. 86 1982 592 627
15. J.D. Murray A pattern formation mechanism and its application to mammalian coat markings Lect. Notes in Biomathematics Volume 39 1980 Springer Boston, MA 360 399
16. J.D. Murray On pattern formation mechanism for lepidopteran wing patterns and mammalian coat markings Phil. Trans. Roy. Soc. B295 1981 473 496