Competition models for plant stems

The models introduced in this paper describe a uniform distribution of plant stems competing for sunlight. The shape of each stem, and the density of leaves, are designed in order to maximize the captured sunlight, subject to a cost for transporting water and nutrients from the root to all the leave...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 269; no. 2; pp. 1571 - 1611
Main Authors Bressan, Alberto, Galtung, Sondre T., Reigstad, Audun, Ridder, Johanna
Format Journal Article
LanguageEnglish
Published Elsevier Inc 05.07.2020
Subjects
Competitive equilibrium
Nonlinear boundary value problem
Optimal shape
Nonlinear boundary value problem
34B15
92B05
49N90
Optimal shape
91A40
Competitive equilibrium
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Summary:The models introduced in this paper describe a uniform distribution of plant stems competing for sunlight. The shape of each stem, and the density of leaves, are designed in order to maximize the captured sunlight, subject to a cost for transporting water and nutrients from the root to all the leaves. Given the intensity of light, depending on the height above ground, we first solve the optimization problem determining the best possible shape for a single stem. We then study a competitive equilibrium among a large number of similar plants, where the shape of each stem is optimal given the shade produced by all others. Uniqueness of equilibria is proved by analyzing the two-point boundary value problem for a system of ODEs derived from the necessary conditions for optimality.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2020.01.013