Generating Functions of Stochastic L-Systems and Application to Models of Plant Development

Cedric Loi 1, 2 Paul Henry Cournède 2, 1
2 DIGIPLANTE - Modélisation de la croissance et de l'architecture des plantes
MAS - Mathématiques Appliquées aux Systèmes - EA 4037, Inria Saclay - Ile de France, Ecole Centrale Paris, CIRAD - Centre de Coopération Internationale en Recherche Agronomique pour le Développement
Abstract : If the interest of stochastic L-systems for plant growth simulation and visualization is broadly acknowledged, their full mathematical potential has not been taken advantage of. In this article, we show how to link stochastic L-systems to multitype branching processes, in order to characterize the probability distributions and moments of the numbers of organs in plant structure. Plant architectural development can be seen as the combination of two subprocesses driving the bud population dynamics, branching and differentiation. By writing the stochastic L-system associated to each subprocess, we get the generating function associated to the whole system by compounding the associated generating functions. The modelling of stochastic branching is classical, but to model differentiation, we introduce a new framework based on multivariate phase-type random vectors.
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Cedric Loi, Paul Henry Cournède. Generating Functions of Stochastic L-Systems and Application to Models of Plant Development. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. pp.325-338. ⟨hal-01194661⟩

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