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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. R. Bravo de la Parra. Dispersal and Total Population Size in Discrete-Time
Metapopulation Models, Mathematics, 2026,
14, 3624. https://doi.org/10.3390/math14193624. (PDF)
2. L. Sanz-Lorenzo, R. Bravo de la Parra, JC.
Poggiale, P. Auger. Multi-Compartmental
Staged Progression Endemic Models with Fast Transitions, Journal of Mathematical Biology, 91,
49, 2025. https://doi.org/10.1007/s00285-025-02291-0. (PDF)
3. R. Bravo de la Parra, E. Venturino, A discrete two time scales
model of a size-structured population of parasitized trees, Mathematical Biosciences and Engineering, 21(9):7040-7066,
2024. https://doi.org/mbe.2024309. (PDF)
4. L. Sanz-Lorenzo, R. Bravo de la Parra, Discrete-time staged progression epidemic models, Mathematical and Computer Modelling of Dynamical
Systems, 30(1): 496-522, 2024.
https://doi.org/10.1080/13873954.2024. (PDF)
5.
J.-C. Poggiale, R. Bravo de la Parra, E. Venturino, The role of manipulative trophically transmitted
parasites in the stability of a predator–prey community, Nonlinear
Analysis: Real World Applications, 79,
104123, 2024. https://doi.org/10.1016/j.nonrwa.2024. (PDF)
6.
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. https://doi.org/10.1007/s10980-024-01792-5. (PDF)
7.
R. Bravo de
la Parra, Reduction of discrete-time infectious disease models, Mathematical Methods in the Applied Sciences,
2023:1-19, 2023. https://doi.org/10.1002/mma9186. (PDF)
8.
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. https://doi.org/10.1051/mmnp/2023004 (PDF)
9.
R. Bravo de
la Parra, L. Sanz, Discrete epidemic models with two
time scales, Advances
in Difference Equations, 2021:478, 2021. https://doi.org/10.1186/s13662-021-03633-0. (PDF)
10.
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. https://doi.org/10.1016/j.ecolmodel.2019.108829. (PDF)
11.
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. https://doi.org/10.3934/dcdsb.2019204. (PDF)
12.
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. https://doi.org/10.1186/s13662-019-2303-1. (PDF)
13.
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. https://doi.org/10.1051/mmnp/2018034. (PDF)
14.
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. https://doi.org/10.1155/2017/5310837. (PDF)
15.
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)
16.
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)
17. 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)
18.
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)
19.
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)
20.
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)
21.
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)
22.
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)
23.
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)
24.
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)
25.
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)
26.
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)
27.
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)
28.
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)
29.
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)
30.
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)
31.
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)
32.
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)
33.
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)
34.
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)
35.
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)
36.
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)
37.
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)
38.
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)
39.
L. Sanz, R.
Bravo de la Parra, Approximate
reduction of multiregional models with environmental stochasticity, Mathematical
Biosciences, 206(1):134-154,
2007. (PDF)
40.
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)
41.
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)
42.
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)
43.
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)
44.
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)
45.
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)
46.
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)
47.
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)
48.
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)
49.
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)
50.
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)
51.
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)
52.
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)
53.
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)
54.
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)
55.
L. Sanz, R.
Bravo de la Parra, Time scales
in stochastic multiregional models, Nonlinear Analysis: Real World Applications,
1:89-122, 2000. (PDF)
56.
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)
57.
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)
58.
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)
59.
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)
60.
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)
61.
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)
62.
L. Sanz, R.
Bravo de la Parra, Variables
aggregation in a time discrete linear model, Mathematical Biosciences, 157(1-2):91-109, 1999. (PDF)
63.
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)
64.
L. Sanz, R.
Bravo de la Parra, Variables
Aggregation in Time Varying Discrete Systems, Acta Biotheoretica,
46:273-297, 1998. (PDF)
65.
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)
66.
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)
67.
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)
68.
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)
69.
R. Bravo de
la Parra, E. Sánchez, Aggregation Methods in Population Dynamics Discrete Models, Mathematical
and Computer Modelling, 27(4):23-39,
1998. (PDF)
70.
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)
71.
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)
72.
Sánchez, R.
Bravo de la Parra, P. Auger, Linear
Discrete Models with Different Time-Scales, Acta Biotheoretica, 43:465-479,
1995. (PDF)
73.
R. Bravo de
la Parra, P. Auger, E. Sánchez, Aggregation Methods in Discrete Models, Journal of
Biological Systems, 3:603-612,
1995. (PDF)
74.
R. Bravo de
la Parra, A. Fernández, On the Valiron Deficiencies of Oriented
Functions, Mathematica
Scandinavica, 69:31-44, 1991. (PDF)
75.
R. Bravo de la Parra, P.
Jiménez-Guerra, Linear Operators and Vector Integrals, Mathematica Japonica,
36:255-262, 1991. (PDF)
76.
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)
77.
R. Bravo de la Parra, Espacios Lp y teoremas de convergencia para integrales vectoriales, Collectanea Mathematica, 38:65-76, 1987. (PDF)