T. Fourcaud, X. Zhang, A. Stokes, H. Lambers, and C. Korner, Plant Growth Modelling and Applications: The Increasing Importance of Plant Architecture in Growth Models, Annals of Botany, vol.101, issue.8, pp.1053-1063, 2008.
DOI : 10.1093/aob/mcn050

URL : https://hal.archives-ouvertes.fr/halsde-00281936

R. Sievänen, E. Nikinmaa, P. Nygren, H. Ozier-lafontaine, J. Perttunen et al., Components of functional-structural tree models, Annals of Forest Science, vol.57, issue.5, pp.399-412, 2000.
DOI : 10.1051/forest:2000131

P. Prusinkiewicz, Modeling plant growth and development, Current Opinion in Plant Biology, vol.7, issue.1, pp.79-84, 2004.
DOI : 10.1016/j.pbi.2003.11.007

J. Perttunen, R. Sievänen, E. Nikinmaa, H. Salminen, H. Saarenmaa et al., LIGNUM: A Tree Model Based on Simple Structural Units, Annals of Botany, vol.77, issue.1, pp.87-98, 1996.
DOI : 10.1006/anbo.1996.0011

C. Godin and Y. Caraglio, A Multiscale Model of Plant Topological Structures, Journal of Theoretical Biology, vol.191, issue.1, pp.1-46, 1998.
DOI : 10.1006/jtbi.1997.0561

URL : https://hal.archives-ouvertes.fr/hal-00827484

W. Kurth, Specifications of morphological models with Lsystems and relational growth grammars, Journal of Interdisciplinary Image Science, vol.5, 2007.

G. Lopez, R. Favreau, C. Smith, P. Costes, T. Prusinkiewicz et al., Integrating simulation of architectural development and source???sink behaviour of peach trees by incorporating Markov chains and physiological organ function submodels into L-PEACH, Functional Plant Biology, vol.35, issue.10, pp.761-771, 2008.
DOI : 10.1071/FP08039

URL : https://hal.archives-ouvertes.fr/hal-00831808

E. Costes, C. Smith, Y. Renton, P. Guédon, C. Prusinkiewicz et al., MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models, Functional Plant Biology, vol.35, issue.10, pp.936-950, 2008.
DOI : 10.1071/FP08081

URL : https://hal.archives-ouvertes.fr/hal-00831809

J. Perttunen, R. Sievänen, and E. Nikinmaa, LIGNUM: a model combining the structure and the functioning of trees, Ecological Modelling, vol.108, issue.1-3, pp.189-198, 1998.
DOI : 10.1016/S0304-3800(98)00028-3

B. Zheng, L. Shi, Y. Ma, Q. Deng, B. Li et al., Comparison of architecture among different cultivars of hybrid rice using a spatial light model based on 3-D digitising, Functional Plant Biology, vol.35, issue.10, pp.900-910, 2008.
DOI : 10.1071/FP08060

M. Cieslak, C. Lemieux, J. Hanan, and P. Prusinkiewicz, Quasi-Monte Carlo simulation of the light environment of plants, Functional Plant Biology, vol.35, issue.10, pp.837-849, 2008.
DOI : 10.1071/FP08082

C. Robert, C. Fournier, B. Andrieu, and B. Ney, epidemic model (Septo3D): a new approach to investigate plant???pathogen interactions linked to canopy architecture, Functional Plant Biology, vol.35, issue.10, pp.997-1013, 2008.
DOI : 10.1071/FP08066

URL : https://hal.archives-ouvertes.fr/hal-01192058

H. Yan, M. Kang, P. De-reffye, and M. Dingkuhn, A Dynamic, Architectural Plant Model Simulating Resource-dependent Growth, Annals of Botany, vol.93, issue.5, pp.591-602, 2004.
DOI : 10.1093/aob/mch078

URL : https://hal.archives-ouvertes.fr/inria-00122497

P. Cournède, M. Kang, A. Mathieu, J. Barczi, H. Yan et al., Structural Factorization of Plants to Compute Their Functional and Architectural Growth, SIMULATION, vol.82, issue.7, pp.427-438, 2006.
DOI : 10.1177/0037549706069341

P. Prusinkiewicz, Modeling of spatial structure and development of plants: a review, Scientia Horticulturae, vol.74, issue.1-2, pp.113-149, 1998.
DOI : 10.1016/S0304-4238(98)00084-3

M. Kang, P. Cournède, J. Quadrat, and P. De-reffye, A Stochastic Language for Plant Topology, 2006 Second International Symposium on Plant Growth Modeling and Applications, 2006.
DOI : 10.1109/PMA.2006.57

C. Loi and P. Cournède, Generating functions of stochastic L-systems and application to models of plant development, Discrete Mathematics and Theoretical Computer Science Proceedings, vol.AI, pp.325-338, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01194661

W. Kurth, Some new formalisms for modelling the interactions between plant architecture, competition and carbon allocation, 4th workshop on individual-based structural and functional models in ecology. Wallenfels, Bayreuther forumökologieforum¨forumökologie, 1996.

D. Barthélémy, Y. Caraglio, and E. Costes, Architecture, gradients morphogénétiques etâgeet?etâge physiologique chez les végétaux, " in Modélisation et simulation de l'architecture des végétaux, ser, Sciences Update, J. Bouchon, pp.89-136, 1997.

Y. Zhang, D. Reed, P. Cattelino, M. Gale, E. Jones et al., A process-based growth model for young red pine, Forest Ecology and Management, vol.69, issue.1-3, pp.21-40, 1994.
DOI : 10.1016/0378-1127(94)90217-8

P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, 1990.
DOI : 10.1007/978-1-4613-8476-2

M. Kang, P. De-reffye, J. Barczi, B. Hu, and F. Houllier, Stochastic 3D tree simulation using substructure instancing, Plant Growth Models and Applications PMA03, pp.154-168, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00121486

A. Mathieu, P. Cournede, V. Letort, D. Barthelemy, and P. De-reffye, A dynamic model of plant growth with interactions between development and functional mechanisms to study plant structural plasticity related to trophic competition, Press, pp.54-55, 2009.
DOI : 10.1093/aob/mcp054

URL : https://hal.archives-ouvertes.fr/halsde-00418643

P. De-reffye, M. Goursat, J. Quadrat, and B. Hu, The dynamic equations of the tree morphogenesis GreenLab model, Plant Growth Models and Applications, pp.108-117, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00071706

Y. Guo, Y. Ma, Z. Zhan, B. Li, M. Dingkuhn et al., Parameter Optimization and Field Validation of the Functional-Structural Model GREENLAB for Maize, Annals of Botany, vol.97, issue.2, pp.217-230, 2006.
DOI : 10.1093/aob/mcj033

URL : https://hal.archives-ouvertes.fr/hal-00018867

D. Chauveheid, Formalisation etétudeet´etétude d'un système complexe dans la théorie des systèmes dynamiques, 2008.

A. Mathieu, P. Cournède, D. Barthélémy, and P. De-reffye, Rhythms and Alternating Patterns in Plants as Emergent Properties of a Model of Interaction between Development and Functioning, Annals of Botany, vol.101, issue.8, pp.1233-1242, 2008.
DOI : 10.1093/aob/mcm171

URL : https://hal.archives-ouvertes.fr/halsde-00288730

R. M. Corless, G. H. Gonnet, D. E. Hare, D. J. Jeffrey, and D. E. Knuth, On the LambertW function, Advances in Computational Mathematics, vol.1, issue.6, pp.329-359, 1996.
DOI : 10.1007/BF02124750

V. Grange, GreenLab mathematical model behavior analysis on Roux architectural model, 2006.

R. M. Corless, D. E. Jeffrey, and D. J. Knuth, function, Proceedings of the 1997 international symposium on Symbolic and algebraic computation , ISSAC '97, pp.197-204, 1997.
DOI : 10.1145/258726.258783

R. Sievänen and T. Burk, Fitting process-based models with stand growth data: problems and experiences, Forest Ecology and Management, vol.69, issue.1-3, pp.145-156, 1994.
DOI : 10.1016/0378-1127(94)90225-9

H. Bossel, treedyn3 forest simulation model, Ecological Modelling, vol.90, issue.3, pp.187-227, 1996.
DOI : 10.1016/0304-3800(95)00139-5

A. Mäkelä, A carbon balance model of growth and selfpruning in trees based on structural relationships, Forest Science, vol.43, issue.1, pp.7-24, 1997.

C. R. Schwalm and A. R. Ek, A process-based model of forest ecosystems driven by meteorology, Ecological Modelling, vol.179, issue.3, pp.317-348, 2004.
DOI : 10.1016/j.ecolmodel.2004.04.016

A. H. Ftter, T. Stickland, M. L. Harvey, and G. Wilson, Architectural analysis of plant root systems 1. Architectural correlates of exploitation efficiency, New Phytologist, vol.34, issue.3, pp.375-382, 1991.
DOI : 10.1016/S0092-8240(83)80056-1

V. Letort, P. Cournède, A. Mathieu, P. De-reffye, and T. Constant, ), Functional Plant Biology, vol.35, issue.10, pp.951-963, 2008.
DOI : 10.1071/FP08065