TY - JOUR
T1 - Competition models for plant stems
AU - Bressan, Alberto
AU - Galtung, Sondre T.
AU - Reigstad, Audun
AU - Ridder, Johanna
N1 - Funding Information:
The research of A. Bressan was partially supported by NSF , with grant DMS-1714237 , “Models of controlled biological growth”. S.T. Galtung was supported in part by a grant from the U.S.-Norway Fulbright Foundation . A. Reigstad was supported by the grant “Waves and Nonlinear Phenomena” ( 250070 ) from the Research Council of Norway . S.T. Galtung and A. Reigstad are very grateful to the Department of Mathematics at Penn State University for the generous hospitality during the academic year 2018/2019.
Funding Information:
The research of A. Bressan was partially supported by NSF, with grant DMS-1714237, ?Models of controlled biological growth?. S.T. Galtung was supported in part by a grant from the U.S.-Norway Fulbright Foundation. A. Reigstad was supported by the grant ?Waves and Nonlinear Phenomena? (250070) from the Research Council of Norway. S.T. Galtung and A. Reigstad are very grateful to the Department of Mathematics at Penn State University for the generous hospitality during the academic year 2018/2019.
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/7/5
Y1 - 2020/7/5
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jde.2020.01.013
DO - 10.1016/j.jde.2020.01.013
M3 - Article
AN - SCOPUS:85078063606
SN - 0022-0396
VL - 269
SP - 1571
EP - 1611
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -