Home, Research, Editions, Vita, MiscLinks

 

 

PUBLICATIONS:

 

Rafael Bravo de la Parra

Catedrático de Universidad de Matemática Aplicada

U.D. Matemáticas, Universidad de Alcalá,

28871 Alcalá de Henares, Madrid, Spain

rafael.bravo@uah.es

 

BOOK CHAPTERS

 

  1. P. Auger, R. Bravo de la Parra, J.C. Poggiale, E. Sánchez, T. Nguyen Huu, Aggregation of variables and applications to population dynamics. In: P. Magal, S. Ruan (Eds.), Structured Population Models in Biology and Epidemiology, Lecture Notes in Mathematics, vol. 1936, Mathematical Biosciences Subseries. Springer, Berlin, 2008, p. 209-263.

 

 

JOURNAL ARTICLES

 

  1. 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)
  2. 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)
  3. 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)
  4. 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)
  5. 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)
  6. 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)
  7. 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)
  8. 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)
  9. 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)
  10. 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)
  11. 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)
  12. 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)
  13. 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)
  14. 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)
  15. 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)
  16. 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)
  17. 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)
  18. 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)
  19. 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)
  20. 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)
  21. 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)
  22. 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)
  23. 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)
  24. 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)
  25. 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)
  26. 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)
  27. 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)
  28. 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)
  29. 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)
  30. 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)
  31. L. Sanz, R. Bravo de la Parra, Approximate reduction of multiregional models with environmental stochasticity, Mathematical Biosciences, 206(1):134-154, 2007. (PDF)
  32. 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)
  33. 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)
  34. 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)
  35. 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)
  36. 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)
  37. 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)
  38. 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)
  39. 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)
  40. 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)
  41. 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)
  42. 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)
  43. 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)
  44. 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)
  45. 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)
  46. 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)
  47. L. Sanz, R. Bravo de la Parra, Time scales in stochastic multiregional models, Nonlinear Analysis: Real World Applications, 1:89-122, 2000. (PDF)
  48. 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)
  49. 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)
  50. 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)
  51. 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)
  52. 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)
  53. 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)
  54. L. Sanz, R. Bravo de la Parra, Variables aggregation in a time discrete linear model, Mathematical Biosciences, 157(1-2):91-109, 1999. (PDF)
  55. 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)
  56. L. Sanz, R. Bravo de la Parra, Variables Aggregation in Time Varying Discrete Systems, Acta Biotheoretica, 46:273-297, 1998. (PDF)
  57. 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)
  58. 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)
  59. 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)
  60. 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)
  61. R. Bravo de la Parra, E. Sánchez, Aggregation Methods in Population Dynamics Discrete Models, Mathematical and Computer Modelling, 27(4):23-39, 1998. (PDF)
  62. 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)
  63. 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)
  64. Sánchez, R. Bravo de la Parra, P. Auger, Linear Discrete Models with Different Time-Scales, Acta Biotheoretica, 43:465-479, 1995. (PDF)
  65. R. Bravo de la Parra, P. Auger, E. Sánchez, Aggregation Methods in Discrete Models, Journal of Biological Systems, 3:603-612, 1995. (PDF)
  66. R. Bravo de la Parra, A. Fernández, On the Valiron Deficiencies of Oriented Functions, Mathematica Scandinavica, 69:31-44, 1991. (PDF)
  67. R. Bravo de la Parra, P. Jiménez-Guerra, Linear Operators and Vector Integrals, Mathematica Japonica, 36:255-262, 1991. (PDF)
  68. 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)
  69. R. Bravo de la Parra, Espacios Lp y teoremas de convergencia para integrales vectoriales, Collectanea Mathematica, 38:65-76, 1987. (PDF)