L. Abbadie, J. Gignoux, X. Le-roux, and M. Lepage, Lamto: structure, functioning, and dynamics of a Savanna Ecosystem, 2006.
URL : https://hal.archives-ouvertes.fr/bioemco-00175292

, Biomath, vol.7, p.1812167, 2018.

F. Accatino and C. De-michele, Humid savanna-forest dynamics: A matrix model with vegetation-fire interactions and seasonality, Ecol. Modell, vol.265, issue.0, pp.170-179, 2013.

F. Accatino and C. De-michele, Interpreting woody cover data in tropical and subtropical areas: Comparison between the equilibrium and the non-equilibrium assumption, Eco. Comp, vol.25, pp.60-67, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01532548

F. Accatino, C. De-michele, R. Vezzoli, D. Donzelli, and R. Scholes, Tree-grass co-existence in savanna: interactions of rain and fire, J. Theor. Biol, vol.267, pp.235-242, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00629962

F. Accatino, K. Wiegand, D. Ward, and C. De-michele, Trees, grass, and fire in humid savannas: The importance of life history traits and spatial processes, Ecol. Modell, vol.320, pp.135-144, 2016.

R. Anguelov, Y. Dumont, and J. M. Lubuma, On nonstandard finite difference schemes in biosciences, AIP Conf. Proc, vol.1487, pp.212-223, 2012.

S. Archibald, D. P. Roy, B. Van-wilgen, and R. J. Scholes, What limits fire? an examination of drivers of burnt area in southern africa, Global Change Biol, vol.15, pp.613-630, 2009.

P. Augier, C. Lett, and J. C. Poggiale, Modelisation mathematique en ecologie. Cours et exercices corrigés. Dunod, 2010.

I. Backéus, Distribution and vegetation dynamics of humid savannas in Africa and Asia, J. Veg. Sci, vol.3, issue.3, pp.345-356, 1992.

N. Barbier, P. Couteron, R. Lefever, V. Deblauwe, and O. Lejeune, Spatial decoupling of facilitation and competition at the origin of gapped vegetation patterns, Ecology, vol.89, pp.1521-1531, 2008.
URL : https://hal.archives-ouvertes.fr/halsde-00291831

M. Baudena, F. D'andrea, and A. Provenzale, An idealized model for tree-grass coexistence in savannas: the role of life stage structure and fire disturbances, J. Ecol, vol.98, pp.74-80, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01136716

M. Baudena, S. C. Dekker, P. M. Van-bodegom, B. Cuesta, S. I. Higgins et al., savannas and grasslands: bridging the knowledge gap between ecology and dynamic global vegetation models, Biogeosciences Discuss, vol.11, pp.9471-9510, 2014.

B. Beckage, L. J. Gross, and W. J. Platt, Grass feedbacks on fire stabilize savannas, Ecol. Modell, vol.222, pp.2227-2233, 2011.

B. Beckage, W. Platt, and L. Gross, Vegetation, fire and feedbacks: a disturbance-mediated model of savannas, Am. Nat, vol.174, issue.6, pp.805-818, 2009.

A. J. Belsky, Influuences of trees on savanna productivity: tests of shade, nutrients and tree-grass competition, Ecology, vol.75, pp.922-932, 1994.

A. J. Belsky, R. G. Amundson, J. M. Duxbury, S. J. Rika, A. R. Ali et al., The effects of trees on their physical, chemical, and biological environment in a semi-arid savanna in Kenya, J. Appl. Ecol, vol.26, pp.1005-1024, 1989.

W. J. Bond, What limits trees in C4 grasslands and savannas ?, Annu. Rev. Ecol. Evol. Syst, vol.39, pp.641-659, 2008.

W. J. Bond and J. E. Keeley, Fire as a global "herbivore":the ecology and evolution of flammable ecosystems, Trends in Ecoloy and Evolution, vol.20, issue.7, pp.387-394, 2005.

W. J. Bond and G. F. Midgley, A proposed CO2controlled mechanism of woody plant invasion in grasslands and savannas, Global Change Biol, vol.6, pp.865-869, 2000.

W. J. Bond, G. F. Midgley, and F. I. Woodward, What controls south african vegetation-climate or fire? S

. J. Afr and . Bot, , vol.69, pp.30362-30370, 2003.

W. J. Bond and C. J. Parr, Beyond the forest edge: Ecology, diversity and conservation of the grassy biomes, Biol. Conserv, vol.143, pp.2395-2404, 2010.

W. J. Bond, F. I. Woodward, and G. F. Midgley, The global distribution of ecosystems in a world without fire, New Phytol, vol.165, pp.525-538, 2005.

F. Borgogno, P. D'odorico, F. Laio, and L. Ridolfi, Mathematical models of vegetation pattern formation in ecohydrology, Rev. Geophys, vol.47, p.1005, 2009.

A. Bouvet, S. Mermoz, T. L. Toan, L. Villard, R. Mathieu et al., An aboveground biomass map of african savannahs and woodlands at 25m resolution derived from alos palsar. Remote Sensing of Environment, vol.206, pp.156-173, 2018.

J. Brookman-amissah, J. B. Hall, J. M. Swaine, and . Attakorah, A re-assessment of a fire protection experiment in north-eastern Ghana savanna, Journal of Applied Ecology, vol.17, issue.1, pp.85-99, 1980.

G. Bucini and N. P. Hanan, A continental-scale analysis of tree cover in african savannas, Global Ecol

, Biomath, vol.7, p.1812167, 2018.

I. V. Yatat-djeumen, A. Tchuinté-tamen, Y. Dumont, and P. Couteron, A tribute to the use of minimalistic

. Biogeogr, , vol.16, pp.593-605, 2007.

A. Cuni-sanchez, L. J. White, K. Calders, K. J. Jeffery, K. Abernethy et al., African savannaforest boundary dynamics: A 20-year study, PLoS One, vol.11, issue.6, p.156934, 2016.

C. De-michele, F. Accatino, R. Vezzoli, and R. J. Scholes, Savanna domain in the herbivores-fire parameter space exploiting a tree-grass-soil water dynamic model, J. Theor. Biol, vol.289, issue.0, pp.74-82, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00739263

A. Dhooge, W. Govaerts, and Y. A. Kuznetsov, MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs, ACM TOMS, vol.29, issue.2, pp.141-164, 2003.

F. Dietrich, G. Koster, M. Seitz, and I. Von-sivers, Bridging the gap: From cellular automata to differential equation models for pedestrian dynamics, Journal of Computational Science, vol.5, issue.5, pp.841-846, 2014.

A. Diouf, N. Barbier, A. M. Lykke, P. Couteron, V. Deblauwe et al., Relationships between fire history, edaphic factor and woody vegetation structure and composition in a semiarid savanna landscape (niger, west africa), Appl. Veg. Sci, vol.15, pp.488-500, 2012.

P. , F. Laio, and L. Ridolfi, A probabilistic analysis of fire-induced tree-grass coexistence in savannas, Am. Nat, vol.167, issue.3, pp.79-87, 2006.

J. Dohn, F. Dembélé, M. Karembé, A. Moustakas, A. Kosiwa et al., Tree effects on grass growth in savannas: competition, facilitation and the stress-gradient hypothesis, Journal of Ecology, vol.101, issue.1, pp.202-209, 2012.

Y. Dumont, J. Soulie, and F. Michel, Modeling oil palm pollinator dynamics using deterministic and agent-based approaches. applications on fruit set estimates. some preliminary results, Mathematical Methods in the Applied Sciences, issue.0, p.0
URL : https://hal.archives-ouvertes.fr/lirmm-01799376

T. G. Farr, P. A. Rosen, E. Caro, R. Crippen, R. Duren et al., The shuttle radar topography mission, Reviews of Geophysics, vol.45, p.2004, 2007.

C. Favier, J. Aleman, L. Bremond, M. A. Dubois, V. Freycon et al., Abrupt shifts in african savanna tree cover along a climatic gradient, Global Ecol. Biogeogr, vol.21, pp.787-797, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01970158

C. Favier, J. Chave, A. Fabing, D. Schwartz, and M. A. Dubois, Modelling forest-savanna mosaic dynamics in man-influenced environments: effects of fire, climate and soil heterogeneity, Ecol. Modell, vol.171, pp.85-102, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01969801

E. C. February, S. I. Higgins, W. J. Bond, and L. Swemmer, Influence of competition and rainfall manipulation on the growth responses of savanna trees and grasses, Ecology, vol.94, pp.1155-1164, 2013.

P. Frost, E. Medina, J. C. Menaut, O. Solbrig, and B. Walker, Responses of savannas to stress and disturbance, Biology International, vol.10, pp.1-82, 1986.

P. G. Frost and F. Robertson, editor, determinants of tropical savannas, vol.3, pp.93-140, 1985.

J. Gignoux, G. Lahoreau, R. Julliard, and S. Barot, Establishment and early persistence of tree seedlings in an annually burned savanna, Journal of Ecology, vol.97, pp.484-495, 2009.
URL : https://hal.archives-ouvertes.fr/bioemco-00392762

W. Govaerts, Numerical bifurcation analysis for ODEs, J. Comput. Appl. Math, vol.125, issue.1, pp.458-459, 2000.

W. Govaerts, R. K. Ghaziani, Y. A. Kuznetsov, and H. G. Meijer, Numerical methods for two-parameter local bifurcation analysis of maps, SIAM J. Sci. Comput, vol.29, issue.6, pp.2644-2667, 2007.

N. Govender, W. S. Trollope, and B. W. Van-wilgen, The effect of fire season, fire frequency, rainfall and management on fire intensity in savanna vegetation in south africa, J. Appl. Ecol, vol.43, issue.4, pp.748-758, 2006.

S. Higgins, W. J. Bond, and W. Trollope, Fire, resprouting and variability: a recipe for grass-tree coexistence in savanna, Journal of Ecology, vol.88, pp.213-229, 2000.

S. I. Higgins, S. Scheiter, and M. Sankaran, The stability of african savannas: insights from the indirect estimation of the parameters of dynamic model, Ecology, vol.91, pp.1682-1692, 2010.

M. Hirota, M. Holmgren, E. H. Van-nes, and M. Scheffer, Global resilience of tropical forest and savanna to critical transitions, Science, vol.334, issue.6053, pp.232-235, 2011.

W. A. Hoffmann, E. L. Geiger, S. G. Gotsch, D. R. Rossatto, L. C. Silva et al., Ecological thresholds at the savannaforest boundary: how plant traits

, Biomath, vol.7, p.1812167, 2018.

I. V. Yatat-djeumen, A. Tchuinté-tamen, Y. Dumont, and P. Couteron, A tribute to the use of minimalistic ... govern the distribution of tropical biomes, Ecology letters, vol.15, issue.7, pp.759-768, 2012.

R. M. Holdo, R. D. Holt, and J. M. Fryxell, Grazers, browsers, and fire influence the extent and spatial pattern of tree cover in the Serengeti, Ecol. Appl, vol.19, issue.1, pp.95-109, 2009.

C. S. Holling, The components of predation as revealed by a study of small mammal predation on the european pine sawfly, Canadian Entomologist, vol.91, pp.293-320, 1959.

K. J. Jeffery, L. Korte, F. Palla, G. Walters, L. J. White et al., Fire management in a changing landscape: a case study from lope national park, gabon. Parks, vol.20, pp.39-52, 2014.

D. N. Karger, O. Conrad, J. Bohner, T. Kawohl, K. Kreft et al., Climatologies at high resolution for the earth's land surface areas. Scientific Data, 4, 2017.

A. Klausmeier, Regular and irregular patterns in semiarid vegetation, Science, vol.284, pp.1826-1828, 1999.

P. Klimasara and M. Tyran-kami´nskakami´nska, A model for random fire induced tree-grass coexistence in savannas

. Arxiv, , pp.1-8, 2018.

R. Lefever, N. Barbier, P. Couteron, and O. Lejeune, Deeply gapped vegetation patterns: Oncrown/root allometry, criticality and desertification, J. Theo. Ecol, vol.261, pp.194-209, 2009.

R. Lefever and O. Lejeune, On the origin of tiger bush, Bul. Math. Biol, vol.59, pp.263-294, 1997.

R. Lefever and J. W. Turner, A quantitative theory of vegetation patterns based on plant structure and the non-local F-KPP equation, C. R. Mecanique, vol.340, pp.818-828, 2012.

C. Lehmann, S. Archibald, W. A. Hoffmann, and W. J. Bond, Deciphering the distribution of the savanna biome, New Phytol, vol.191, pp.197-209, 2011.

R. Martinez-garcia, J. M. Calabrese, E. Hernandezgarcia, and C. Lopez, Minimal mechanisms for vegetation patterns in semiarid regions, Phil. Trans. R. Soc. A, vol.372, 2014.

P. Mayaux, E. Bartholomé, S. Fritz, and A. Belward, A new land-cover map of africa for the year 2000, J. Biogeogr, vol.31, issue.6, pp.861-877, 2004.

S. J. Mcnaughton, The propagation of disturbance in savannas through food webs, J. Veg. Sci, vol.3, issue.3, pp.301-314, 1992.

S. J. Mcnaughton and N. J. Georgiadis, Ecology of african grazing and browsing mammals, vol.17, pp.39-66, 1986.

J. C. Menaut and J. Cesar, Structure and primary productivity of lamto savannas, ivory coast, Ecology, vol.60, pp.1197-1210, 1979.

S. Mermoz, T. Le-toan, L. Villard, M. Réjou-méchan, and J. Seifert-granzin, Biomass assessment in the cameroon savanna using alos palsar data. Remote Sening of Environment, 2014.

S. Mermoz, M. Réjou-méchan, L. Villard, T. Le-toan, V. Rossi et al., Decrease of Lband SAR backscatter with biomass of dense forests, Remote Sening of Environment, vol.159, pp.307-317, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01902422

E. Meron, Pattern-formation approach to modelling spatially extended ecosystems, Ecol. Model, 2011.

E. Meron, E. Gilad, J. Von, M. Hardenberg, Y. Shachak et al., Vegetation patterns along a rainfall gradient, Chaos Solitons Fractals, vol.19, issue.2, pp.49-52, 2004.

E. T. Mitchard and C. M. Flintrop, Woody encroachment and forest degradation in sub-saharan africa's woodlands and savannas 1982-2006, Philos. Trans. R. Soc. Lond. B. Biol. Sci, vol.368, 2013.

E. T. Mitchard, S. S. Saatchi, S. L. Lewis, T. R. Feldpausch, I. H. Woodhouse et al., Measuring biomass changes due to woody encroachment and deforestation/degradation in a forestsavanna boundary region of central africa using multitemporal l-band radar backscatter. Remote Sensing of Environment, vol.115, pp.2861-2873, 2011.

A. Moustakas, W. E. Kunin, T. C. Cameron, and M. Sankaran, Facilitation or competition ? Tree effects on grass biomass across a precipitation gradient, PLoS One, vol.8, p.57025, 2013.

P. Narbel, Qualitative and Quantitative Cellular Automata from Differential Equations, vol.4173, pp.112-121, 2006.

I. Oliveras and Y. Malhi, Many shades of green: the dynamic tropical forest-savannah transition zones, Phil. Trans. R. Soc. B, vol.371, 2016.

S. Omohundro, Modelling cellular automata with Biomath, vol.7, p.1812167, 2018.

I. V. Yatat-djeumen, A. Tchuinté-tamen, Y. Dumont, and P. Couteron, A tribute to the use of minimalistic ... partial differential equations, Physica D: Nonlinear Phenomena, vol.10, issue.1, pp.128-134, 1984.

R. Oslisly, L. White, I. Bentaleb, C. Favier, M. Fontugne et al., Climatic and cultural changes in the west congo basin forests over the past 5000 years, Phil. Trans. R. Soc. B, vol.368, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01970011

M. Sankaran, N. P. Hanan, R. J. Scholes, J. Ratnam, D. J. Augustine et al., Determinants of woody coverin african savannas, Nature, vol.438, pp.846-849, 2005.

G. Sarmiento, The Ecology of Neotropical Savannas, 1984.

S. Scheiter and S. I. Higgins, Partitioning of root and shoot competition and the stability of savannas, Am. Nat, vol.179, pp.587-601, 2007.

R. J. Scholes, Convex relationships in ecosystems containing mixtures of trees and grass. Environnemental and Ressource Economics, vol.26, pp.559-574, 2003.

R. J. Scholes and S. R. Archer, Tree-grass interactions in savannas, Annu. Rev. Ecol. Syst, vol.28, pp.517-544, 1997.

R. J. Scholes and B. Walker, An African Savanna: Synthesis of the Nylsvley Study, 1993.

J. A. Sherratt, An analysis of vegetation stripe formation in semi-arid landscapes

, J. Math. Biol, vol.51, pp.183-197, 2005.

C. Skarpe, Shrub layer dynamics under different herbivore densities in an arid savanna, botswana, Journal of Applied Ecology, vol.27, issue.3, pp.873-885, 1990.

A. C. Staver, S. Archibald, and S. Levin, Tree cover in sub-saharan Africa: Rainfall and fire constrain forest and savanna as alternative stable states, Ecology, vol.92, issue.5, pp.1063-1072, 2011.

A. C. Staver and S. Levin, Integrating theoretical climate and fire effects on savanna and forest systems, Am. Nat, vol.180, p.14, 2012.

A. D. Synodinos, B. Tietjen, and F. Jeltsch, Facilitation in drylands: Modeling a neglected driver of savanna dynamics, Ecol. Modell, vol.304, pp.11-21, 2015.

A. D. Synodinos, B. Tietjen, D. Lohmann, and F. Jeltsch, The impact of inter-annual rainfall variability on african savannas changes with mean rainfall, Journal of Theoretical Biology, vol.437, pp.92-100, 2018.

A. Tchuinté-tamen, Study of a Generic Mathematical Model of Forest-Savanna Interactions: Case of Cameroon, 2017.

A. Tchuinté-tamen, P. Couteron, and Y. Dumont, Effect of fire frequency and rainfall on tree-grass dynamics: Capturing the forest-savanna distributions at biogeographic scale, 2018.

A. Tchuinté-tamen, Y. Dumont, J. J. Tewa, S. Bowong, and P. Couteron, Tree-grass interaction dynamics and pulsed fires: mathematical and numerical studies, Appl. Math. Mod, vol.40, pp.6165-6197, 2016.

A. Tchuinté-tamen, Y. Dumont, J. J. Tewa, S. Bowong, and P. Couteron, A minimalistic model of tree-grass interactions using impulsive differential equations and non-linear feedback functions of grass biomass onto fire-induced tree mortality, Math. Comput. Simul, vol.133, pp.265-297, 2017.

A. Tchuinté-tamen, J. J. Tewa, P. Couteron, S. Bowong, and Y. Dumont, A generic modeling of fire impact in a tree-grass savanna model, Biomath, vol.3, p.1407191, 2014.

J. J. Tewa, I. V. Yatat-djeumen, and S. Bowong, Predator-prey model with holling response function of type ii and sis infectious disease, Appl. Math. Modell, vol.37, issue.7, pp.4825-4841, 2013.

K. Thonicke, S. Venevsky, S. Sitch, and W. Cramer, The role of fire disturbance for global vegetation dynamics: coupling fire into a dynamic global vegetation model, Global Ecol. Biogeogr, vol.10, issue.6, pp.661-677, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01757654

D. Tilman, Competition and biodiversity in spatially structured habitats, Ecology, vol.75, issue.1, pp.2-16, 1994.

M. Torello-raventos, T. R. Feldpausch, K. Veenendaal, F. Schrodt, G. Saiz et al., Biomath, vol.7, p.1812167, 2018.

S. L. Lewis, O. L. Phillips, and J. Lloyd, On the delineation of tropical vegetation types with an emphasis on forest/savanna transitions, Plant Ecology & Diversity, vol.6, issue.1, pp.101-137, 2013.

J. D. Touboul, C. Staver, and S. A. Levin, On the complex dynamics of savanna landscapes, Proceedings of the National Academy of Sciences, 2018.

W. S. Trollope, Fire in savanna, Ecological Effects of Fire in South African Ecosystems, pp.149-175, 1984.

W. S. Trollope, Personal perspectives on commercial versus communal african fire paradigms when using fire to manage rangelands for domestic livestock and wildlife in southern and east african ecosystems, Fire Ecology, vol.7, issue.1, pp.57-73, 2011.

W. S. Trollope and L. A. Trollope, Fire in african savanna and other grazing ecosystems. paper presented at the seminar on 'forest fire and global change' held in shshenkoye in the russian federation, pp.4-10, 1996.

W. S. Trollope and L. A. Trollope, Fire effects and management in african grasslands and savannas, Range and Animal Sci. Resour. Manag, vol.2, pp.121-145, 2010.

F. Van-langevelde, C. Van-de-vijver, L. Kumar, J. Van-de-koppel, N. D. Rider et al., Effects of fire and herbivory on the stability of savanna ecosystems, Ecology, vol.84, issue.2, pp.337-350, 2003.

B. W. Van-wilgen, N. Govender, H. C. Biggs, D. Ntsala, and X. N. Funda, Response of savanna fire regimes to changing fire-management policies in a large african national park, Conserv. Biol, vol.18, pp.1537-1540, 2004.

B. Walker, D. Ludwig, C. S. Holling, and R. M. Peterman, Stability of semi-arid savanna grazing systems, Journal of Ecology, vol.69, issue.2, pp.473-498, 1981.

B. Walker and I. Noy-meir, Aspects of the stability and resilience of savanna ecosystems, Ecology of tropical savannas, pp.555-590, 1982.

H. Walter, Ecology of tropical and subtropical vegetation, 1971.

J. R. Weimar, Cellular automata for reaction-diffusion systems, Parallel Computing, vol.23, issue.11, pp.81-82, 1997.

J. F. Weltzin and M. B. Coughenour, Savanna tree influence on understory vegetation and soil nutrients in northwestern Kenya, J. Veg. Sci, vol.1, pp.325-334, 1990.

S. Wolfram, Twenty problems in the theory of cellular automata, Physica Scripta, issue.T9, p.170, 1985.

V. Yatat, P. Couteron, and Y. Dumont, Spatially explicit modelling of tree-grass interactions in fireprone savannas: a partial differential equations framework, Ecol. Compl, pp.290-313, 2018.

V. Yatat, P. Couteron, J. J. Tewa, S. Bowong, and Y. Dumont, An impulsive modelling framework of fire occurrence in a size-structured model of treegrass interactions for savanna ecosystems, J. Math. Biol, vol.74, issue.6, pp.1425-1482, 2017.

V. Yatat and Y. Dumont, FKPP equation with impulses on unbounded domain, Mathematical Methods and Models in Biosciences, 2018.

V. Yatat, Y. Dumont, J. J. Tewa, P. Couteron, and S. Bowong, Mathematical analysis of a size structured tree-grass competition model for savanna ecosystems, Biomath, vol.3, p.1404212, 2014.
URL : https://hal.archives-ouvertes.fr/hal-02078416

I. V. Yatat-djeumen, Mathematical analysis of sizestructured tree-grass interactions models for savanna ecosystems, 2018.

J. and Y. Happi, Arbres contre graminées: la lente invasion de la savane par la forêt au Centre-Cameroun, 1998.

K. Yu and P. , An eco-hydrological framework for grass displacement by woody plants in savannas, J. Geophys. Res. Biogeosci, vol.119, pp.192-206, 2014.

, Biomath, vol.7, p.1812167, 2018.