Temporal organization in a morphogenetic field. (English) Zbl 0549.92001

Granero-Porati, M. I.; Porati, A.

J. Math. Biol. 20, 153-157 (1984).

Summary: We have investigated the possibility of self-sustained oscillations of chemical concentrations during morphogenetic processes. In particular, we have shown that, in the case of the A. Gierer and H. Meinhardt [Kybernetik 12, No. 1, 30–39 (1972; Zbl 1434.92013)] self-sustained oscillations are possible when an order parameter, connected with the decay constants of morphogenes, crosses a critical value. The analytical results are in agreement with the numerical results of Gierer and Meinhardt.

MSC:

92B05	General biology and biomathematics
34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
92C15	Developmental biology, pattern formation

Keywords:

limit cycle; biological clocks; Gierer-Meinhardt model; self-sustained oscillations of chemical concentrations; morphogenetic processes

Citations:

Zbl 1434.92013