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1. | Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino |
References:
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doi: 10.1007/s00285-010-0369-1. |
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F. Cerretti, B. Perthame, C. Schmeiser, M. Tang and N. Vauchelet, Branching instabilities in Hyperbolic Keller-Segel systems, Math. Models Methods Appl. Sci., 21 (2011), 825-842. |
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D. Challet, M. Marsili and Y. C. Zhang, "Minority Games: Interacting Agents in Financial Markets," Oxford Finance, 2005. |
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M. Delitala and T. Lorenzi, Asymptotic dynamics in continuous structured populations with mutations, competition and mutualism, Journal of Mathematical Analysis and Applications, 389 (2012), 439-451.
doi: 10.1016/j.jmaa.2011.11.076. |
[5] |
M. Delitala and T. Lorenzi, Recognition and learning in a mathematical model for immune response against cancer, Discrete and Continuous Dynamical Systems - Series B, to appear.
doi: 10.3934/dcdsb.2013.18.891. |
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L. Desvillettes, P. E. Jabin, S. Mischler and G. Raoul, On selection dynamics for continuous structured populations, Communications in Mathematical Sciences, 6 (2008), 729-747.
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O. Diekmann, P. E. Jabin, S. Mischler and B. Perthame, The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach, Theoretical Population Biology, 67 (2005), 257-271.
doi: 10.1016/j.tpb.2004.12.003. |
[8] |
M. Gauduchon and B. Perthame, Survival thresholds and mortality rates in adaptive dynamics: conciliating deterministic and stochastic simulations, Mathematical Medicine and Biology, 27 (2010), 195-210.
doi: 10.1093/imammb/dqp018. |
[9] |
S. Genieys, V. Volpert and P. Auger, Pattern and waves for a model in population dynamics with nonlocal consumption of resources, Mathematical Modelling of Natural Phenomena, 1 (2006), 65-82.
doi: 10.1051/mmnp:2006004. |
[10] |
S. A. H. Geritz, E. Kisdi, G. Meszena, J. A. J. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evol. Ecol., 12 (1998) 35-57. |
[11] |
S. A. H. Geritz, J. A. J.Metz, E. Kisdi and G. Meszena, Dynamics of adaptation and evolutionary branching, Phys. Rev. Lett., 78 (1997), 2024-2027.
doi: 10.1103/PhysRevLett.78.2024. |
[12] |
D. Hanahan and R. A. Weinberg, Hallmarks of cancer: the next generation, Cell, 144 (2011), 646-674.
doi: 10.1016/j.cell.2011.02.013. |
[13] |
A. Lorz, S. Mirrahimi and B. Perthame, Dirac mass dynamics in multidimensional nonlocal parabolic equations, Communications in Partial Differential Equations, 36 (2011), 1071-1098.
doi: 10.1080/03605302.2010.538784. |
[14] |
J. Maynard Smith, "Evolution and the Theory of Games," Cambridge University Press, 1982. |
[15] |
S. Mirrahimi, B. Perthame and J. Wakano, Evolution of species trait through resource competition, Journal of Mathematical Biology, 64 (2012), 1189-1223.
doi: 10.1007/s00285-011-0447-z. |
[16] |
G. Naldi, L. Pareschi and G. Toscani (Eds.), "Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences," Birkhäuser, Basel, 2010.
doi: 10.1007/978-0-8176-4946-3. |
[17] |
J. C. Nuno, M. Primicerio and M. A. Herrero, A mathematical model of a criminal-prone society, DCDS-S, 4 (2011), 193-207.
doi: 10.3934/dcdss.2011.4.193. |
[18] |
K. Painter and T. Hillen, Spatio-temporal chaos in a chemotaxis model, Physica D: Nonlinear Phenomena, 240 (2011), 363-375.
doi: 10.1016/j.physd.2010.09.011. |
[19] |
B. Perthame, "Transport Equations in Biology," Birkhäuser, Basel, 2007. |
[20] |
V. Quaranta, K. A. Rejniak, P. Gerlee and A. R. Anderson, Invasion emerges from cancer cell adaptation to competitive microenvironments: quantitative predictions from multiscale mathematical models, Seminars in Cancer Biology, 18 (2008), 338-348.
doi: 10.1016/j.semcancer.2008.03.018. |
[21] |
V. Semeshenko, M. B. Gordon and J. P. Nadal, Collective states in social systems with interacting learning agents, Physica A: Statistical Mechanics and its Applications, 387 (2008), 4903-4916.
doi: 10.1016/j.physa.2008.04.019. |
[22] |
Z. Wang and T. Hillen, Classical solutions and pattern formation for a volume filling chemotaxis model, Chaos, 17 (2007), 037108.
doi: 10.1063/1.2766864. |
show all references
References:
[1] |
V. Andasari, A. Gerisch, G. Lolas, A. P. South and M. A. J. Chaplain, Mathematical modeling of cancer cell invasion of tissue: Biological insight from mathematical analysis and computational simulation, Journal of Mathematical Biology, 63 (2011), 141-171.
doi: 10.1007/s00285-010-0369-1. |
[2] |
F. Cerretti, B. Perthame, C. Schmeiser, M. Tang and N. Vauchelet, Branching instabilities in Hyperbolic Keller-Segel systems, Math. Models Methods Appl. Sci., 21 (2011), 825-842. |
[3] |
D. Challet, M. Marsili and Y. C. Zhang, "Minority Games: Interacting Agents in Financial Markets," Oxford Finance, 2005. |
[4] |
M. Delitala and T. Lorenzi, Asymptotic dynamics in continuous structured populations with mutations, competition and mutualism, Journal of Mathematical Analysis and Applications, 389 (2012), 439-451.
doi: 10.1016/j.jmaa.2011.11.076. |
[5] |
M. Delitala and T. Lorenzi, Recognition and learning in a mathematical model for immune response against cancer, Discrete and Continuous Dynamical Systems - Series B, to appear.
doi: 10.3934/dcdsb.2013.18.891. |
[6] |
L. Desvillettes, P. E. Jabin, S. Mischler and G. Raoul, On selection dynamics for continuous structured populations, Communications in Mathematical Sciences, 6 (2008), 729-747.
doi: 10.4310/CMS.2008.v6.n3.a10. |
[7] |
O. Diekmann, P. E. Jabin, S. Mischler and B. Perthame, The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach, Theoretical Population Biology, 67 (2005), 257-271.
doi: 10.1016/j.tpb.2004.12.003. |
[8] |
M. Gauduchon and B. Perthame, Survival thresholds and mortality rates in adaptive dynamics: conciliating deterministic and stochastic simulations, Mathematical Medicine and Biology, 27 (2010), 195-210.
doi: 10.1093/imammb/dqp018. |
[9] |
S. Genieys, V. Volpert and P. Auger, Pattern and waves for a model in population dynamics with nonlocal consumption of resources, Mathematical Modelling of Natural Phenomena, 1 (2006), 65-82.
doi: 10.1051/mmnp:2006004. |
[10] |
S. A. H. Geritz, E. Kisdi, G. Meszena, J. A. J. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evol. Ecol., 12 (1998) 35-57. |
[11] |
S. A. H. Geritz, J. A. J.Metz, E. Kisdi and G. Meszena, Dynamics of adaptation and evolutionary branching, Phys. Rev. Lett., 78 (1997), 2024-2027.
doi: 10.1103/PhysRevLett.78.2024. |
[12] |
D. Hanahan and R. A. Weinberg, Hallmarks of cancer: the next generation, Cell, 144 (2011), 646-674.
doi: 10.1016/j.cell.2011.02.013. |
[13] |
A. Lorz, S. Mirrahimi and B. Perthame, Dirac mass dynamics in multidimensional nonlocal parabolic equations, Communications in Partial Differential Equations, 36 (2011), 1071-1098.
doi: 10.1080/03605302.2010.538784. |
[14] |
J. Maynard Smith, "Evolution and the Theory of Games," Cambridge University Press, 1982. |
[15] |
S. Mirrahimi, B. Perthame and J. Wakano, Evolution of species trait through resource competition, Journal of Mathematical Biology, 64 (2012), 1189-1223.
doi: 10.1007/s00285-011-0447-z. |
[16] |
G. Naldi, L. Pareschi and G. Toscani (Eds.), "Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences," Birkhäuser, Basel, 2010.
doi: 10.1007/978-0-8176-4946-3. |
[17] |
J. C. Nuno, M. Primicerio and M. A. Herrero, A mathematical model of a criminal-prone society, DCDS-S, 4 (2011), 193-207.
doi: 10.3934/dcdss.2011.4.193. |
[18] |
K. Painter and T. Hillen, Spatio-temporal chaos in a chemotaxis model, Physica D: Nonlinear Phenomena, 240 (2011), 363-375.
doi: 10.1016/j.physd.2010.09.011. |
[19] |
B. Perthame, "Transport Equations in Biology," Birkhäuser, Basel, 2007. |
[20] |
V. Quaranta, K. A. Rejniak, P. Gerlee and A. R. Anderson, Invasion emerges from cancer cell adaptation to competitive microenvironments: quantitative predictions from multiscale mathematical models, Seminars in Cancer Biology, 18 (2008), 338-348.
doi: 10.1016/j.semcancer.2008.03.018. |
[21] |
V. Semeshenko, M. B. Gordon and J. P. Nadal, Collective states in social systems with interacting learning agents, Physica A: Statistical Mechanics and its Applications, 387 (2008), 4903-4916.
doi: 10.1016/j.physa.2008.04.019. |
[22] |
Z. Wang and T. Hillen, Classical solutions and pattern formation for a volume filling chemotaxis model, Chaos, 17 (2007), 037108.
doi: 10.1063/1.2766864. |
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