Analysis of dynamical model of plant growth analysis in calculus

The model suggested in this work is based on the following biological facts and mathematical approximations: a). The growing part of the plant, or apex, contains a narrow exterior part, the meristem where cells proliferate providing the plant growth. This layer has a constant width and consists of an approximately constant number of cell layers specific to each plant. Since it is very small compared to the whole plant, it will be considered as a mathematical surface. The displacement of this surface corresponds to the plant growth. b). The appearance of new cells implies that old cells exit this external layer after some time and become a part of the internal plant tissue. They differentiate, that is, they change their functions. They cannot divide any more, and they serve to conduct nutrients to the meristem. c). The proliferation rate is determined by the concentration of nutrients and of GM-factors in the meristem. The GM-factors are produced in the meristem. The rate of their production is selfaccelerationg. They can be transmitted between neighboring cells. d). Appearance of new buds is determined by concentrations of certain plant hormones .