Pattern formation in noisy self-replicating spots

International Journal of Bifurcation and Chaos

Volumn 16, Issue 12, 2006, Pages 3679-3685

  Munteanu, Andreea ^a   Solé, Ricard V ^b  

^a UNIVERSITAT POMPEU FABRA   (Spain)

^b SANTA FE INSTITUTE   (United States)

Author keywords

Noise; Prebiotic evolution; Reaction diffusion; Self replication; Turing patterns

Indexed keywords

DIFFUSION; MATHEMATICAL MODELS; OPTIMIZATION; SHRINKAGE; SPURIOUS SIGNAL NOISE;

PREBIOTIC EVOLUTION; TURING PATTERNS;

PATTERN RECOGNITION;

EID: 33847244910     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406017063     Document Type: Article

References (17)

1. Boerlijst, M. C. [2000] "Spirals and spots: Novel evolutionary phenomena through spatial self-structuring," in The Geometry of Ecological Interactions: Simplifying Spatial Complexity, eds. Dieckmann, U., Law, R. & Metz, J. (Cambridge University Press, Cambridge) pp. 171-182.
2. Cross, M. & Hohenberg, P. [1993] "Pattern formation outside of equilibrium," Rev. Mod. Phys. 65, 851-1112.
3. Gierer, A. & Meinhardt, H. [2000] "Theory of biological pattern formation," Kybernetik 12, 30-39.
4. Gray, P. & Scott, S. K. [1985] "Sustained oscillations and other exotic patterns of behavior in isothermal reactions," J. Phys. Chem. 89, 22-32.
5. Hochberg, D., Lesmes, F., Moran, F. & Perez-Mercader, J. 120031 "Large-scale emergent properties of an auto-catalytic reaction-diffusion model subject to noise," Phys. Rev. E 68, 066114.1-066114.10.
6. Koch, A. J. & Meinhardt, H. [1994] "Biological pattern formation: From basic mechanisms to complex structures," Rev. Mod. Phys. 66, 1481-1507.
7. Lee, K. J., McCormick, W. D., Ouyang, Q. & Swinney, H. L. [1993] "Pattern formation by interacting chemical fronts," Science 261, 192-194.
8. Lee, K. J., McCormick, W. D., Swinney, H. L. & Pearson, J. E. [1994] "Experimental observation of self-replicating spots in a reaction-diffusion system," Nature 369, 215-218.
9. Lesmes, F., Hochberg, D., Moran, F. & Perez-Mercader, J. [2003] "Noise-controlled self-replicating patterns," Phys. Rev. Lett. 91, 238301.1-238301.4.
10. Mazin, W., Rasmussen, K. E., Mosekilde, E., Borckmans, P. & Dewel, G. [1996] "Pattern formation in the bistable Gray-Scott model," Math. Comput. Simul. 40, 371-396.
11. Muratov, C. B. & Osipov, V. V. [2000] "Static spike autosolitons in the Gray-Scott model," J. Phys. A: Math. Gen. 33, 8893-8916.
12. Pearson, J. E. [1993] "Complex patterns in a simple system," Science 261, 189-192.
13. Rovinsky, A. & Menzinger, M. [1992] "Interaction of Turing and Hopf bifurcation in chemical systems," Phys. Rev. A 46, 6315-6322.
14. Segel, L. A. & Jackson, J. L. [1972] "Dissipative structure: An explanation and an ecological example," J. Theor. Biol. 37, 545-549.
15. Strogatz, S. [1994] Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering (Addison-Wesley, Reading, MA).
16. Takagi, H. & Kaneko, K. [2002] "Pattern dynamics of a multi-component reaction-diffusion system: Differentiation of replicating spots," Int. J. Bifurcation and Chaos 12, 2579-2598.
17. Turing, J. E. [1952] "The chemical basis of morphogenesis," Philos. Trans. Roy. Soc. London Ser. B 327, 37-72.