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A hyperbolic model of spatial evolutionary game theory
| 1. | Dipartimento di Scienze Applicate - Università di Napoli "Parthenope", Via A. De Gasperi, 5 - 80133 Napoli, Italy |
| 2. | Dipartimento di Scienze di Base e Applicate per l’Ingegneria (SBAI), Università degli Studi “Sapienza” di Roma |
| 3. | Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, c/o Department of Mathematics, University of Rome “Tor Vergata”, Via della Ricerca Scientifica, 1; I-00133 Roma |
References:
| [1] |
A. L. Amadori, A. Boccabella and R. Natalini, A one dimensional hyperbolic model for evolutionary game theory: numerical approximations and simulations, Commun. Appl. Ind. Math., 1 (2010), 1-21.
doi: DOI: 10.1685/2010CAIM494. |
| [2] |
D. Ambrosi and L. Preziosi, On the closure of mass balance models for tumour growth, Math. Models Methods Appl. Sci., 12 (2002), 737-754. |
| [3] |
A. Bressan, Hyperbolic systems of conservation laws. The one-dimensional Cauchy problem, Oxford Lecture Series in Mathematics and its Applications, 20 (2000). |
| [4] |
M. C. Cattaneo, Sur une forme de l'equation de la chaleur liminant le paradoxe d'une propagation instantane, Comptes Rendus L'Acad. Sci. Ser. I-Math., 247 (1958), 431-433. |
| [5] |
K. N. Chueh and C. C. Conley and J. A. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana Univ. Math. J., 26 (1977), 373-392. |
| [6] |
R. Cressman and G. T. Vickers, Spatial and density effects in evolutionary game theory, J. Theor. Biol., 184 (1997), 359-369. |
| [7] |
R. Ferriere and R. E. Michod, The evolution of cooperation in spatially heterogeneous populations, The American Naturalist, 147 (1996), 692-717 |
| [8] |
F. Fu, M. A. Nowak and Ch. Hauert, Invasion and expansion of cooperators in lattice populations: Prisoner's dilemma vs. Snowdrift games, J. Theor. Biol., 266 (2010), 358-366
doi: DOI: 10.1016/j.jtbi.2010.06.042. |
| [9] |
T. Hillen, Hyperbolic models for chemosensitive movement, Math. Models Methods Appl. Sci., 12 (2002), 1007-1034. |
| [10] |
T. Hillen, On the $L^2$-moment closure of transport equations: the Cattaneo approximation, Discrete Cont. Dyn. Syst., B4 (2004), 961-982. |
| [11] |
J. Hofbauer and K. Sigmund, "Evolutionary Games and Population Dynamics," Cambridge University Press, 1998.
doi: DOI: 10.1090/S0273-0979-03-00988-1. |
| [12] |
J. Hofbauer and K. Sigmund, Evolutionary game dynamics, B. Am. Math. Soc., 40 (2003), 479-519. |
| [13] |
V. C. L. Hutson and G. T. Vickers, Travelling waves and dominance of ESS's, J. Math. Biol., 30 (1992), 457-471. |
| [14] |
J. Maynard Smith, "Evolution and the Theory of Games," Cambridge University Press, 1982. |
| [15] |
J. Maynard Smith and G. R. Price, The logic of animal conflicts, Nature, 246 (1973), 15-18. |
| [16] |
J. Fort and V. Mendez, Wavefronts in time-delayed reaction-diffusion systems. Theory and comparison to experiment, Rep. Prog. Phys., 65 (2002), 895-954. |
| [17] |
V. Mendez, S. Fedotov and W. Horsthemke, "Reaction-transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities Series: Springer Series in Synergetics,", 2010., ().
|
| [18] |
J. D. Murray, "Mathematical Biology. II. Spatial Models and Biomedical Applications," Third edition. Interdisciplinary Applied Mathematics, 18. Springer-Verlag, New York, 2003. xxvi+811 pp. |
| [19] |
J. Nash, Non-cooperative games, Ann. of Math., 54 (1951), 286-295. |
| [20] |
M. A. Nowak, "Evolutionary Dynamics," Harvard University Press, 2001. |
| [21] |
M. E. Taylor, "Partial Differential Equations III. Nonlinear Equations," Second edition. Applied Mathematical Sciences, 117. Springer, New York, 2011. xxii+715 pp. |
| [22] |
P. D. Taylor and L. B. Jonker, Evolutionary stable strategies and game dynamics, Math. Biosci., 40 (2001), 145-156. |
| [23] |
G. T. Vickers, Spatial patterns and ESS's, J. Theor. Biol., 140 (1989), 129-135. |
show all references
References:
| [1] |
A. L. Amadori, A. Boccabella and R. Natalini, A one dimensional hyperbolic model for evolutionary game theory: numerical approximations and simulations, Commun. Appl. Ind. Math., 1 (2010), 1-21.
doi: DOI: 10.1685/2010CAIM494. |
| [2] |
D. Ambrosi and L. Preziosi, On the closure of mass balance models for tumour growth, Math. Models Methods Appl. Sci., 12 (2002), 737-754. |
| [3] |
A. Bressan, Hyperbolic systems of conservation laws. The one-dimensional Cauchy problem, Oxford Lecture Series in Mathematics and its Applications, 20 (2000). |
| [4] |
M. C. Cattaneo, Sur une forme de l'equation de la chaleur liminant le paradoxe d'une propagation instantane, Comptes Rendus L'Acad. Sci. Ser. I-Math., 247 (1958), 431-433. |
| [5] |
K. N. Chueh and C. C. Conley and J. A. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana Univ. Math. J., 26 (1977), 373-392. |
| [6] |
R. Cressman and G. T. Vickers, Spatial and density effects in evolutionary game theory, J. Theor. Biol., 184 (1997), 359-369. |
| [7] |
R. Ferriere and R. E. Michod, The evolution of cooperation in spatially heterogeneous populations, The American Naturalist, 147 (1996), 692-717 |
| [8] |
F. Fu, M. A. Nowak and Ch. Hauert, Invasion and expansion of cooperators in lattice populations: Prisoner's dilemma vs. Snowdrift games, J. Theor. Biol., 266 (2010), 358-366
doi: DOI: 10.1016/j.jtbi.2010.06.042. |
| [9] |
T. Hillen, Hyperbolic models for chemosensitive movement, Math. Models Methods Appl. Sci., 12 (2002), 1007-1034. |
| [10] |
T. Hillen, On the $L^2$-moment closure of transport equations: the Cattaneo approximation, Discrete Cont. Dyn. Syst., B4 (2004), 961-982. |
| [11] |
J. Hofbauer and K. Sigmund, "Evolutionary Games and Population Dynamics," Cambridge University Press, 1998.
doi: DOI: 10.1090/S0273-0979-03-00988-1. |
| [12] |
J. Hofbauer and K. Sigmund, Evolutionary game dynamics, B. Am. Math. Soc., 40 (2003), 479-519. |
| [13] |
V. C. L. Hutson and G. T. Vickers, Travelling waves and dominance of ESS's, J. Math. Biol., 30 (1992), 457-471. |
| [14] |
J. Maynard Smith, "Evolution and the Theory of Games," Cambridge University Press, 1982. |
| [15] |
J. Maynard Smith and G. R. Price, The logic of animal conflicts, Nature, 246 (1973), 15-18. |
| [16] |
J. Fort and V. Mendez, Wavefronts in time-delayed reaction-diffusion systems. Theory and comparison to experiment, Rep. Prog. Phys., 65 (2002), 895-954. |
| [17] |
V. Mendez, S. Fedotov and W. Horsthemke, "Reaction-transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities Series: Springer Series in Synergetics,", 2010., ().
|
| [18] |
J. D. Murray, "Mathematical Biology. II. Spatial Models and Biomedical Applications," Third edition. Interdisciplinary Applied Mathematics, 18. Springer-Verlag, New York, 2003. xxvi+811 pp. |
| [19] |
J. Nash, Non-cooperative games, Ann. of Math., 54 (1951), 286-295. |
| [20] |
M. A. Nowak, "Evolutionary Dynamics," Harvard University Press, 2001. |
| [21] |
M. E. Taylor, "Partial Differential Equations III. Nonlinear Equations," Second edition. Applied Mathematical Sciences, 117. Springer, New York, 2011. xxii+715 pp. |
| [22] |
P. D. Taylor and L. B. Jonker, Evolutionary stable strategies and game dynamics, Math. Biosci., 40 (2001), 145-156. |
| [23] |
G. T. Vickers, Spatial patterns and ESS's, J. Theor. Biol., 140 (1989), 129-135. |
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