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PUBLICATIONS:
Rafael Bravo de la Parra
Catedrático de Universidad de
Matemática Aplicada
U.D.
Matemáticas, Universidad de Alcalá,
28871 Alcalá de Henares, Madrid,
Spain
BOOK
CHAPTERS
JOURNAL
ARTICLES
1. M.A. Zavala, Ó. Angulo, R. Bravo de la Parra, D.
Moreno-Fernández, J. Madrigal-González, Scaling up tree growth to assess forest resilience under
increasing aridity: the case of Iberian dry-edge pine forests, Landscape Ecology, 39, 6, 2024. doi.org/10.1007/s10980-024-01792-5. (PDF)
2. R. Bravo de la Parra, Reduction of
discrete-time infectious disease models, Mathematical Methods in the Applied Sciences,
2023:1-19, 2023. doi.org/10.1002/mma9186. (PDF)
3. R. Bravo de la Parra, J.-C. Poggiale, P. Auger, The effect of connecting sites in the environment of a
harvested population, Mathematical
Modelling of Natural Phenomena, 18, 4, 2023. doi.org/10.1051/mmnp/2023004 (PDF)
4. R. Bravo de la Parra, L. Sanz, Discrete epidemic models with two time scales, Advances in Difference Equations, 2021:478,
2021. doi.org/10.1186/s13662-021-03633-0. (PDF)
5. L. Sanz, R. Bravo de la Parra, Stochastic matrix metapopulation models with fast
migration: re-scaling survival to the fast scale, Ecological Modelling, 418, 2020,
108829.
doi.org/10.1016/j.ecolmodel.2019.108829. (PDF)
6. R. Bravo de la Parra, L. Sanz, A Discrete Model of Competing Species Sharing a
Parasite, Discrete and Continuous Dynamical Systems
Series B, 25(6):2121-2142, 2020. Doi:10.3934/dcdsb.2019204. (PDF)
7. L. Sanz, R. Bravo de la Parra, M. Marvá, E.
Sánchez, Non-linear Population Discrete Models with Two Time Scales: Re-scaling of Part of the Slow
Process, Advances
in Difference Equations, 2019:401, 2019.
doi.org/10.1186/s13662-019-2303-1. (PDF)
8. M. Marvá, R. Bravo de la Parra, E. Venturino, Modelling the Role of Opportunistic Diseases in
Coinfection, Mathematical
Modelling of Natural Phenomena, 13(3): 28, 2018. doi.org/10.1051/mmnp/2018034. (PDF)
9. R. Bravo de la Parra, M. Marvá, E. Sánchez, L. Sanz, Discrete Models of Disease and Competition, Discrete Dynamics in Nature and Society, 2017:
5310837, 2017. doi.org/10.1155/2017/5310837. (PDF)
10.
R. Bravo de
la Parra, M. Marvá,
E. Sánchez, L. Sanz, A Discrete
Predator-Prey Ecoepidemic Model, Mathematical Modelling of Natural Phenomena, 12(2):116-132,
2017. (PDF)
11.
R. Bravo de la Parra, M. Marvá,
F. Sansegundo, Fast Dispersal in Semelparous Populations, Mathematical
Modelling of Natural Phenomena, 11(4):121-135, 2016. (PDF)
12. M. Marvá, E. Venturino, R. Bravo de la Parra, A Time Scales Approach to Coinfection by Opportunistic
Diseases, Journal of Applied Mathematics, 2015:275485, 2015. (PDF)
13. M. Marvá, R. Bravo de la Parra, Coexistence and superior competitor exclusion in the
Leslie–Gower competition model with fast dispersal, Ecological
Modelling, 306:247-256, 2015. (PDF)
14. M. Marvá, J.G. Alcázar, J.-C. Poggiale, R. Bravo de
la Parra, A simple
geometrical condition for the existence of periodic solutions of planar
periodic systems. Applications to some biological models, Journal of
Mathematical Analysis and Applications, 423(2):1469-1479, 2015. (PDF)
15.
M. Marvá, R.
Bravo de la Parra, Reduction of
nonautonomous population dynamics models with two time scales, Acta
Biotheoretica, 62(3): 285-303,
2014. (PDF)
16.
E. Sánchez,
H. Hbid, R. Bravo de la Parra, Mathematical
Analysis of a Population Model with an Age-weight Structured Two-stage Life
History: Asymptotic Behaviour of Solutions, Journal of Evolution Equations,
14(3): 603-616, 2014. (PDF)
17.
R. Bravo de
la Parra, M. Marvá, E. Sánchez, L. Sanz, Reduction of Discrete Dynamical Systems with Applications
to Dynamics Population Models, Mathematical Models of Natural Phenomena, 8(6):
107–129, 2013. (PDF)
18.
O. Angulo, R.
Bravo de la Parra, J.C. López-Marcos, M.A. Zavala, Stand dynamics and tree coexistence in an analytical structured model:
the role of recruitment, Journal of Theoretical Biology, 333(1):91-101, 2013. (PDF)
19.
M. Marvá, R.
Bravo de la Parra, J.-C. Poggiale, Reduction of slow-fast asymptotically autonomous systems with
applications to gradostat models, Ecological Complexity, 14(1):75-84, 2013. (PDF)
20.
M. Marvá,
A. Moussaoui, R. Bravo de la Parra, P. Auger, A density dependent model describing age structured population dynamics
using hawk-dove tactics, Journal of
Difference Equations and Applications, 19(6):1022-1034, 2013. (PDF)
21.
M. Marvá,
J.-C. Poggiale, R. Bravo de la Parra, Reduction of slow-fast periodic systems with applications to population
dynamics models, Mathematical Models and Methods in Applied Sciences, 22(12):1250025, 2012. (PDF)
22.
M. Marvá, R.
Bravo de la Parra, P. Auger, Reproductive
Numbers for Nonautonomous Spatially Distributed Periodic SIS Models Acting on
Two Time Scales, Acta Biotheoretica, 60(1-2):139-154,
2012. (PDF)
23.
M. Marvá, R.
Bravo de la Parra, J.-C. Poggiale, Approximate aggregation of a two time scales periodic multi-strain SIS
epidemic model: A patchy environment with fast migrations, Ecological
Complexity, 10(1):34-41, 2012. (PDF)
24.
T. Nguyen
Huu, R. Bravo de la Parra, P. Auger, Approximate aggregation of linear discrete models with two time-scales:
re-scaling slow processes to the fast scale, Journal of Difference Equations
and Applications, 17(4):621-635,
2011. (PDF)
25.
P. Ruiz
Benito, J.A. Cuevas, R. Bravo de la Parra, J.M. García del Barrio, M.A.
Zavala, Land use change in a Mediterranean
metropolitan region and its periphery: assessment of conservation policies
through CORINE Land Cover data and Markov models, Forest Systems, 19(3):315-328, 2010. (PDF)
26.
D. Nguyen
Ngoc, R. Bravo de la Parra, M.A. Zavala, P. Auger, Competition and species coexistence in a
metapopulation model: Can fast asymmetric migration reverse the outcome of
competition in a homogeneous environment?, Journal of Theoretical Biology,
266:256-263, 2010. (PDF)
27.
A. Kebir,
S. Ben Miled , M.L. Hbid, R. Bravo de la Parra, Effects of density dependent sex allocation on the dynamics of a
simultaneous hermaphroditic population: Modelling and analysis, Journal of
Theoretical Biology, 263:521–529,
2010. (PDF)
28.
M. Marvá,
E. Sánchez, R. Bravo de la Parra, L. Sanz, Reduction of slow–fast discrete models coupling migration and demography, Journal of
Theoretical Biology, 258(3):371-379,
2009. (PDF)
29.
H. Hbid, A.
Kacha, R. Bravo de la Parra, Mathematical
study of a bacteria-fish model with level of infection structure, Nonlinear
Analysis Series B: Real World Applications, 10(3):1662-1678, 2009. (PDF)
30.
P. Auger, R.
Bravo de la Parra, J.C. Poggiale, E. Sánchez, L. Sanz, Aggregation methods in dynamical systems variables and
applications in population and community dynamics, Physics of Life Reviews, 5(2):79-105, 2008. (PDF)
31.
L. Sanz, R.
Bravo de la Parra, E. Sánchez, Approximate
Reduction of Non-Linear Discrete Models with Two Time Scales, Journal of
Difference Equations and Applications, 14(6):607-627,
2008. (PDF)
32.
H. Hbid, E.
Sánchez, R. Bravo de la Parra, State-Dependent
Delays Associated to Threshold Phenomena in Structured Population Dynamics, Mathematical
Models and Methods in Applied Sciences, 17(6):877-900, 2007. (PDF)
33.
El
Abdllaoui, P. Auger, B.W. Kooi, R. Bravo de la Parra, R. Mchich, Effects of density-dependent migrations on stability
of a two-patch predator-prey model, Mathematical Biosciences,
210(1):335-354, 2007. (PDF)
34.
L. Sanz, R.
Bravo de la Parra, Approximate
reduction of multiregional models with environmental stochasticity, Mathematical
Biosciences, 206(1):134-154,
2007. (PDF)
35.
M.A.
Zavala, O. Angulo, R. Bravo de la Parra, J.C. López-Marcos, An analytical model of stand dynamics as a function of
tree growth, mortality and recruitment: The shade tolerance-stand structure
hypothesis revisited, Journal of Theoretical Biology, 244(3):440-450, 2007. (PDF)
36.
E. Sánchez,
R. Bravo de la Parra, P. Auger, P. Gómez Mourelo, Time scales in linear delayed differential equations, Journal of
Mathematical Analysis and Applications, 323(1):680-699, 2006. (PDF)
37.
P. Auger,
B.W. Kooi, R. Bravo de la Parra, J.C. Poggiale, Bifurcation analysis of a predator-prey model with predators using hawk
and dove tactics, Journal of Theoretical Biology, 238(3):587-607, 2006. (PDF)
38.
M.A. Zavala, I.R. Urbieta, R. Bravo de la Parra, O. Angulo,
Modelos
de proceso de la producción y dinámica del bosque mediterráneo, Invest Agrar: Sist Recur For, 14(3):482-496, 2005. (PDF)
39.
M.A.
Zavala, R. Bravo de la Parra, A
mechanistic model of tree competition and facilitation for Mediterranean
forests: scaling from leaf physiology to stand dynamics, Ecological Modelling, 188(1):76-92, 2005. (PDF)
40.
Lett, P.
Auger, R. Bravo de la Parra, Migration
Frequency and the Persistence of Host-Parasitoid Interactions, Journal of
Theoretical Biology, 221:639-654,
2003. (PDF)
41.
L. Sanz, A.
Blasco, R. Bravo de la Parra, Approximate
reduction of multi-type Galton-Watson processes with two time scales, Mathematical
Models and Methods in Applied Sciences, 13(4):491-525, 2003. (PDF)
42.
L. Sanz, R.
Bravo de la Parra, The
Reliability of Approximate Reduction Techniques in Population Models with Two
Time Scales, Acta
Biotheoretica, 50(4):297-322,
2002. (PDF)
43.
R. Mchich,
P. Auger, R. Bravo de la Parra, N. Raïssi, Dynamics of a fishery on two fishing zones with fishing stock dependent
migrations: aggregation and control, Ecological Modelling, 158(1-2):51-62, 2002. (PDF)
44.
A. Blasco,
L. Sanz, R. Bravo de la Parra, Approximate
Reduction of Multiregional Birth-Death Models with Fast Migration, Mathematical
and Computer Modelling, 36:47-65,
2002. (PDF)
45.
P. Auger, R.
Bravo de la Parra, S. Morand, E. Sánchez, A predator-prey model with predators using hawk and dove tactics, Mathematical
Biosciences, 177&178: 185-200, 2002. (PDF)
46.
A. Blasco,
L. Sanz, P. Auger, R. Bravo de la Parra, Linear Discrete Population Models with Two Time Scales in Fast Changing
Environments II: Non-Autonomous Case, Acta Biotheoretica, 50(1):15-38, 2002. (PDF)
47.
A. Blasco,
L. Sanz, P. Auger, R. Bravo de la Parra, Linear Discrete Population Models with Two Time Scales in Fast Changing
Environments I: Autonomous Case, Acta Biotheoretica, 49:261-276, 2001. (PDF)
48.
L. Sanz, R.
Bravo de la Parra, Time scales
in a non-autonomous linear discrete model, Mathematical Models and Methods in Applied
Sciences, 11(7):1203-1235,
2001. (PDF)
49.
P. Auger, R.
Bravo de la Parra, E. Sánchez, Behavioural
dynamics of two interacting hawk-dove populations, Mathematical Models and Methods
in Applied Sciences, 11(4):1-18,
2001. (PDF)
50.
L. Sanz, R.
Bravo de la Parra, Time scales
in stochastic multiregional models, Nonlinear Analysis: Real World Applications,
1:89-122, 2000. (PDF)
51.
P. Auger, R.
Bravo de la Parra, Methods of
aggregation of variables in population dynamics, C. R. Acad. Sci. Paris,
Sciences de la vie, 323:665-674, 2000. (PDF)
52.
Pontier, P.
Auger, R. Bravo de la Parra, E. Sánchez, The impact of behavioural plasticity at individual level on domestic cat
population dynamics, Ecological Modelling, 133:117-124,
2000. (PDF)
53.
S. Charles,
R. Bravo de la Parra, J. P. Mallet, H. Persat, P. Auger, Annual spawning migrations in modeling brown trout
population dynamics inside an arborescent river network, Ecological Modelling, 133:15-31, 2000. (PDF)
54.
R. Bravo de
la Parra, O. Arino, E. Sánchez, P. Auger, A Model for an Age-Structured Population with Two Time
Scales, Mathematical
and Computer Modelling, 31:17-26,
2000. (PDF)
55.
O. Arino, E.
Sánchez, R. Bravo de la Parra, P. Auger, A Singular Perturbation in an Age-Structured Population Model, SIAM Journal
on Applied Mathematics, 60:408-436,
1999. (PDF)
56.
R. Bravo de
la Parra, E. Sánchez, O. Arino, P. Auger, A discrete model with density dependent fast migration, Mathematical
Biosciences, 157(1-2):111-146,
1999. (PDF)
57.
L. Sanz, R.
Bravo de la Parra, Variables
aggregation in a time discrete linear model, Mathematical Biosciences, 157(1-2):91-109, 1999. (PDF)
58.
S. Charles,
R. Bravo de la Parra, J. P. Mallet, H. Persat, P. Auger, A Density Dependent Model Describing Salmo trutta
Population Dynamics in an arborescent river network: effects of dams and
channelling, C.
R. Acad. Sci. Paris, Sciences de la vie, 321:979-990, 1998. (PDF)
59.
L. Sanz, R.
Bravo de la Parra, Variables
Aggregation in Time Varying Discrete Systems, Acta Biotheoretica, 46:273-297, 1998. (PDF)
60.
S. Charles,
R. Bravo de la Parra, J. P. Mallet, H. Persat, P. Auger, Population Dynamics Modelling in an Hierarchical
Arborescent River Network: An Attempt with Salmo trutta, Acta Biotheoretica, 46(3):223-234, 1998. (PDF)
61.
O. Arino,
M. L. Hbid, R. Bravo de la Parra, A mathematical model of growth of population of fish in the larval
stage: Density-dependent effects, Mathematical Biosciences, 150:1-20, 1998. (PDF)
62.
O. Arino,
E. Sánchez, R. Bravo de la Parra, A Model of an Age-Structured Population in a Multipatch Environment, Mathematical
and Computer Modelling, 27(4):137-150,
1998. (PDF)
63.
P. Auger, R.
Bravo de la Parra, E. Sánchez, Hawk-Dove
Game and Competition Dynamics, Mathematical and Computer Modelling, 27(4):89-98, 1998. (PDF)
64.
R. Bravo de
la Parra, E. Sánchez, Aggregation Methods in Population Dynamics Discrete Models, Mathematical
and Computer Modelling, 27(4):23-39,
1998. (PDF)
65.
Sánchez, P.
Auger, R. Bravo de la Parra, Influence
of Individual Agressiveness on the Dynamics of Competitive Populations, Acta
Biotheoretica, 45:321-333, 1997.
(PDF)
66.
R. Bravo de
la Parra, E. Sánchez, P. Auger, Time Scales in Density Dependent Discrete Models, Journal of
Biological Systems, 5:111-129,
1997. (PDF)
67.
Sánchez, R.
Bravo de la Parra, P. Auger, Linear
Discrete Models with Different Time-Scales, Acta Biotheoretica, 43:465-479, 1995. (PDF)
68.
R. Bravo de
la Parra, P. Auger, E. Sánchez, Aggregation Methods in Discrete Models, Journal of
Biological Systems, 3:603-612,
1995. (PDF)
69.
R. Bravo de
la Parra, A. Fernández, On the Valiron Deficiencies of Oriented Functions, Mathematica
Scandinavica, 69:31-44, 1991. (PDF)
70.
R. Bravo de la Parra, P.
Jiménez-Guerra, Linear Operators and Vector Integrals, Mathematica Japonica, 36:255-262,
1991. (PDF)
71.
R. Bravo de la
Parra, Un théorème de
la valeur moyenne pour des intégrales bilinéaires, Les Annales des Sciences
Mathématiques du Québec, 12:179-187,
1988. (PDF)
72.
R. Bravo de la Parra, Espacios Lp
y teoremas de convergencia para integrales vectoriales, Collectanea Mathematica, 38:65-76, 1987. (PDF)