Special Issue on Cooperation, Competition, Organization: The Dynamics of Interacting Living PopulationsNo Access

Cooperation, competition, organization: The dynamics of interacting living populations

Miguel A. Herrero

University Complutense of Madrid, Departamento de Matemática Aplicada, Madrid, Spain

Search for more papers by this author

and

Juan Soler

University of Granada, Departamento de Matemática Aplicada, 18071 Granada, Spain

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0218202515020030Cited by:7 (Source: Crossref)

Abstract

In the following the reader will find a short description of some issues related to the modeling, analysis and simulation of large populations of living systems, a research field which is currently deserving a considerable interest, and that has been explored during the first 10 editions of the BIOMAT Summer School at Granada.

Keywords:

References

J. C. L. Alfonso et al. , Discrete Contin. Dynam. Syst. B 17 , 1651 ( 2012 ) . Crossref, Web of Science, Google Scholar
Ed. P. Ball (ed.) , Why Society is a Complex Matter ( Springer-Verlag , 2012 ) . Crossref, Google Scholar
M. Ballerini et al. , Proc. Natl. Acad. Sci. USA 105 , 1232 ( 2008 ) . Crossref, Web of Science, Google Scholar
A. L. Barabási , The Science of Networks ( Perseus , 2012 ) . Google Scholar
J. Bascompte , Science 329 , 765 ( 2010 ) . Crossref, Web of Science, Google Scholar
N. Bellomo et al. , Math. Models Methods Appl. Sci. 17 , 1675 ( 2007 ) . Link, Web of Science, Google Scholar
N. Bellomo et al. , Math. Models Methods Appl. Sci. 20 , 1179 ( 2010 ) . Link, Web of Science, Google Scholar
N. Bellomo et al. , Math. Models Methods Appl. Sci. 22 , 1130001 ( 2012 ) . Link, Web of Science, Google Scholar
N. Bellomo et al. , Discrete Contin. Dynam. Syst. Ser. B 19 , 1869 ( 2014 ) . Crossref, Web of Science, Google Scholar
N. Bellomo, M. Herrero and A. Tosin, On the dynamics of social conflicts: Looking for the black swan, Kinet. Relat. Models (2013), to appear , arXiv:1202.4554 . Google Scholar
N. Bellomo , B. Piccoli and A. Tosin , Math. Models Methods Appl. Sci. 22 , 1230004 ( 2012 ) . Link, Web of Science, Google Scholar
N. Bellomo and J. Soler , Math. Models Methods Appl. Sci. 22 , 1140006 ( 2012 ) . Link, Web of Science, Google Scholar
N. Bellomo , D. Knopoff and J. Soler , Math. Models Methods Appl. Sci. 23 , 1861 ( 2013 ) . Link, Web of Science, Google Scholar
N. Bellomo and L. Gibelli , Math. Models Methods Appl. Sci. 25 , 2417 ( 2015 ) . Link, Web of Science, Google Scholar
A. Bellouquid , E. De Angelis and D. Knopoff , Math. Models Methods Appl. Sci. 23 , 949 ( 2013 ) . Link, Web of Science, Google Scholar
A. Bellouquid , E. De Angelis and L. Fermo , Math. Models Methods Appl. Sci. 22 , 1140003 ( 2012 ) . Link, Web of Science, Google Scholar
H. Berestycki , F. Hamel and N. Nadirashvili , J. European Math. Soc. 7 , 173 ( 2005 ) . Crossref, Web of Science, Google Scholar
H. Berestycki and L. Rossi , Discrete Contin. Dynam. Syst. 21 , 41 ( 2008 ) . Crossref, Web of Science, Google Scholar
H. Berestycki and F. Hamel , Comm. Pure Appl. Math. 55 , 949 ( 2002 ) . Crossref, Web of Science, Google Scholar
H. Berestycki et al. , Math. Models Methods Appl. Sci. 25 , 2519 ( 2015 ) . Link, Web of Science, Google Scholar
M. Bischoff et al. , Nature Cell Biol. 15 , 1269 ( 2013 ) . Crossref, Web of Science, Google Scholar
L. L. Bonilla et al. , Phys. Rev. Lett. 81 , 3643 ( 1998 ) . Crossref, Web of Science, Google Scholar
T. Cagatay et al. , Cell 139 , 512 ( 2009 ) . Crossref, Web of Science, Google Scholar
J. Calvo et al. , Math. Models Methods Appl. Sci. 21 , 893 ( 2011 ) . Link, Web of Science, Google Scholar
J. Calvo et al. , Math. Models Methods Appl. Sci. 24 , 495 ( 2014 ) . Link, Web of Science, Google Scholar
J. Calvo, J. Campos, V. Caselles, O. S'anchez and J. Soler, Pattern formation in a flux limited reaction-diffusion equation of porous media type , arXiv:1309.6789 . Google Scholar
J. Calvo, J. Campos, V. Caselles, O. Sánchez and J. Soler, Qualitative behavior for flux-saturated mechanisms: Traveling waves, waiting time and smoothing effects, to appear in J. European Math. Soc , arXiv:1402.1679v2 . Google Scholar
J. Campos et al. , Ann. Inst. H. Poincaré Anal. Non Linéaire 30 , 141 ( 2013 ) . Crossref, Web of Science, Google Scholar
F. Cerreti et al. , Math. Models Methods Appl. Sci. 21 , 825 ( 2011 ) . Link, Web of Science, Google Scholar
M. Chaplain et al. , Math. Models Methods Appl. Sci. 21 , 719 ( 2011 ) . Link, Web of Science, Google Scholar
D. Collin et al. , Nature 437 , 231 ( 2005 ) . Crossref, Web of Science, Google Scholar
I. D. Couzin , Nature 445 , 715 ( 2007 ) . Crossref, Web of Science, Google Scholar
P. Degond and S. Motsch , Math. Models Methods Appl. Sci. 18 , 1193 ( 2008 ) . Link, Web of Science, Google Scholar
P. Degond and J.-G. Liu , Math. Models Methods Appl. Sci. 22 , 1140001 ( 2012 ) . Link, Web of Science, Google Scholar
P. Degond and L. Navoret , Math. Models Methods Appl. Sci. 25 , 2439 ( 2015 ) . Link, Web of Science, Google Scholar
E. Dessaud et al. , Nature 450 , 717 ( 2007 ) . Crossref, Web of Science, Google Scholar
C. Espinosa , P. Padilla and E. R. Alvarez-Buylla , Plant Cell. EUA 16 , 2923 ( 2004 ) . Crossref, Web of Science, Google Scholar
A. Fasano , M. A. Herrero and M. R. Rodrigo , Math. Biosci. 220 , 45 ( 2009 ) . Crossref, Web of Science, Google Scholar
A. Fasano et al. , Rev. J. Theor. Biol. 265 , 543 ( 2010 ) . Crossref, Web of Science, Google Scholar
M. Fernandez , V. Milisic and A. Quarteroni , SIAM J. MMS 4 , 215 ( 2005 ) . Crossref, Web of Science, Google Scholar
A. G. Fletcher , P. J. Murray and P. K. Maini , Math. Models Methods Appl. Sci. 25 , 2563 ( 2015 ) . Link, Web of Science, Google Scholar
L. J. Gilarranz and J. Bascompte , J. Theor. Biol. 297 , 11 ( 2012 ) . Crossref, Web of Science, Google Scholar
T. Goudon et al. , J. Differential Equations 213 , 418 ( 2005 ) . Crossref, Web of Science, Google Scholar
G. Th. Guria , M. A. Herrero and K. Zlobina , J. Eng. Math. 66 , 293 ( 2010 ) . Crossref, Web of Science, Google Scholar
C. K. Hemelrijk and H. Hildenbrandt , Ethology 114 , 245 ( 2008 ) . Crossref, Web of Science, Google Scholar
M. A. Herrero , A. Köhn and J. M. Pérez-Pomares , Math. Models Methods Appl. Sci. 19 , 1 ( 2009 ) . Link, Web of Science, Google Scholar
H. Hildenbrandt , C. Carere and C. K. Hemelrijk , Behav. Ecol. 21 , 1349 ( 2010 ) . Crossref, Web of Science, Google Scholar
J. Hofbauer and K. Sigmund , Bull. Amer. Math. Soc. 40 , 479 ( 2003 ) . Crossref, Web of Science, Google Scholar
I. Klapper and J. Dockeryt , SIAM Rev. 52 , 221 ( 2010 ) . Crossref, Web of Science, Google Scholar
S. Kondo and T. Miura , Science 329 , 1616 ( 2010 ) . Crossref, Web of Science, Google Scholar
T. B. Kornberg , Biophys. J. 103 , 2252 ( 2012 ) . Crossref, Web of Science, Google Scholar
A. Koseska et al. , J. Theor. Biol. 263 , 189 ( 2010 ) . Crossref, Web of Science, Google Scholar
E. Mayr , Species and Evolution ( Harward Univ. Press , 1970 ) . Google Scholar
H. Meinhardt , J. Theor. Biol. 74 , 307 ( 1978 ) . Crossref, Web of Science, Google Scholar
H. Meinhardt , Cold Spring Harb. Perspect. Biol. ( 2009 ) , DOI: 10.1101/cshperspect.a001362 . Google Scholar
S. Motsch and E. Tadmor , J. Stat. Phys. 144 , 923 ( 2011 ) . Crossref, Web of Science, Google Scholar
J. Nash , Essentials of Game Theory ( Elgar , 1996 ) . Google Scholar
J. Nieto , F. Poupaud and J. Soler , Arch. Rational Mech. Anal. 158 , 29 ( 2001 ) . Crossref, Web of Science, Google Scholar
M. A. Nowak , Evolutionary Dynamics, Exploring the Equations of Life ( Harvard Univ. Press , 2006 ) . Crossref, Google Scholar
M. A. Nowak and K. Sigmund , Science 303 , 793 ( 2004 ) . Crossref, Web of Science, Google Scholar
J. C. Nuño , M. A. Herrero and M. Primicerio , Discrete Contin. Dynam. Syst. S 4 , 193 ( 2011 ) . Crossref, Web of Science, Google Scholar
D. Ölz and C. Schmeiser , Arch. Rational Mech. Anal. 198 , 963 ( 2010 ) . Crossref, Web of Science, Google Scholar
L. Pareschi and G. Toscani , Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods ( Oxford Univ. Press , 2013 ) . Google Scholar
B. Perthame , C. Quiñinao and J. Touboul , Math. Models Methods Appl. Sci. 25 , 2477 ( 2015 ) . Link, Web of Science, Google Scholar
A. Quarteroni and G. Rozza , Math. Models Methods Appl. Sci. 13 , 1801 ( 2003 ) . Link, Web of Science, Google Scholar
F. A. Ramirez-Weber and T. B. Kornberg , Cell 97 , 599 ( 1999 ) . Crossref, Web of Science, Google Scholar
S. Roy , F. Hsiung and T. B. Kornberg , Science 15 , 354 ( 2011 ) . Crossref, Web of Science, Google Scholar
S. Saavedra et al. , Nature 478 , 233 ( 2011 ) . Crossref, Web of Science, Google Scholar
K. Saha and D. V. Schaffer , Development 133 , 889 ( 2006 ) . Crossref, Web of Science, Google Scholar
F. C. Santos , J. M. Pacheco and T. Lenaerts , Proc. Natl. Acad. Sci. USA 103 , 3490 ( 2006 ) . Crossref, Web of Science, Google Scholar
F. C. Santos et al. , Math. Models Methods Appl. Sci. 22 , 1140004 ( 2012 ) . Link, Web of Science, Google Scholar
B. Stecca and A. Ruiz i Altaba , J. Molec. Cell Biol. 2 , 84 ( 2010 ) . Crossref, Web of Science, Google Scholar
A. Stevens and J. J. L. Velzquez , Nonlinearity 21 , T283 ( 2008 ) . Crossref, Web of Science, Google Scholar
C. E. Tarnita , N. Wage and M. A. Nowak , Proc. Natl. Acad. Sci. 108 , 2334 ( 2011 ) . Crossref, Web of Science, Google Scholar
V. V. Vasconcelos , F. C. Santos and J. M. Pacheco , Math. Models Methods Appl. Sci. 25 , 2503 ( 2015 ) . Link, Web of Science, Google Scholar
V. Vega-Redondo , Complex Social Networks ( Cambridge Univ. Press , 2007 ) . Crossref, Google Scholar
M. Verbeni et al. , Phys. Life Rev. 10 , 457 ( 2013 ) . Crossref, Web of Science, Google Scholar