-
Previous Article
Hopf fibration and singularly perturbed elliptic equations
- DCDS-S Home
- This Issue
-
Next Article
Asymptotic behaviour of sign changing radial solutions of Lane Emden Problems in the annulus
On an initial value problem modeling evolution and selection in living systems
1. | Department of Mathematics and Informatics, University of Perugia, Via Vanvitelli 1, 06123 Perugia, Italy, Italy |
References:
[1] |
D. L. Abel and J. T. Trevors, Self-organization vs. self-ordering events in life-origin models, Physics of Life Reviews, 3 (2006), 221-228.
doi: 10.1016/j.plrev.2006.07.003. |
[2] |
G. Ajmone Marsan, N. Bellomo and M. Egidi, Towards a mathematical theory of complex socio-economical systems by functional subsystems reprsentation, Kinet. Relat. Models, 1 (2008), 249-278.
doi: 10.3934/krm.2008.1.249. |
[3] |
N. Bellomo and B. Carbonaro, Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives, Physics of Life Reviews, 8 (2011), 1-18.
doi: 10.1016/j.plrev.2010.12.001. |
[4] |
N. Bellomo, D. Knopoff and J. Soler, On the difficult interplay between life, "complexity,'' and mathematical sciences, Math. Models Methods Appl. Sci., 23 (2013), 1861-1913.
doi: 10.1142/S021820251350053X. |
[5] |
N. Bellomo, L. Preziosi and G. Forni, On a kinetic (cellular) theory for competition between tumors and the host immune system, J. Biological Systems, 4 (1996), 479-502.
doi: 10.1142/S0218339096000326. |
[6] |
N. Bellomo and J. Soler, On the mathematical theory of the dynamics of swarms viewed as complex systems, Math. Models Methods Appl. Sci., 22 (2012), suppl. 1, 1140006, 29 pp.
doi: 10.1142/S0218202511400069. |
[7] |
A. Belloquid and M. Delitala, Mathematical Modeling of Complex Biological Systems. A Kinetic Theory Approach, Birkhäuser, Boston, 2006.
doi: 10.1007/978-0-8176-4503-8. |
[8] |
A. Bellouquid, E. De Angelis and L. Fermo, Towards the modeling of vehicular traffic as a complex system: A kinetic theory approach, Math. Models Methods Appl. Sci., 22 (2012), suppl. 1, 1140003, 35 pp.
doi: 10.1142/S0218202511400033. |
[9] |
A. Bellouquid, E. De Angelis and D. Knopoff, From the modeling of the immune hallmarks of cancer to a black swan in biology, Math. Models Methods Appl. Sci., 23 (2013), 949-978.
doi: 10.1142/S0218202512500650. |
[10] |
E. L. Cooper, Evolution of immune system from self/not self to danger to artificial immune system (AIS), Physics of Life Reviews, 7 (2010), 55-78.
doi: 10.1016/j.plrev.2009.12.001. |
[11] |
M. Delitala, P. Pucci and M.C. Salvatori, From methods of the mathematical kinetic theory for active particles to modelling virus mutations, Math. Models Methods Appl. Sci., 21 (2011), suppl. 1, 843-870.
doi: 10.1142/S0218202511005398. |
[12] |
S. De Lillo, M. Delitala and M. C. Salvatori, Modelling epidemics and virus mutations by methods of the mathematical kinetic theory for active particles, Math. Models Methods Appl. Sci., 19 (2009), suppl. 1, 1405-1425.
doi: 10.1142/S0218202509003838. |
[13] |
K. Drucis, M. Kolev, W. Majda and B. Zubik-Kowal, Nonlinear modeling with mammographic evidence of carcinoma, Nonlinear Anal. Real World Appl., 11 (2010), 4326-4334.
doi: 10.1016/j.nonrwa.2010.05.017. |
[14] |
R. A. Gatenby and T. L. Vincent, An evolutionary model of carcinogenesis, Cancer Research, 63 (2003), 6212-6220. |
[15] |
R. A. Gatenby, T. L. Vincent and R. J. Gillies, Evolutionary dynamics in carcinogenesis, Math. Models Methods Appl. Sci., 15 (2005), 1619-1638.
doi: 10.1142/S0218202505000911. |
[16] |
D. H. Erwin, Extintion: How Life on Earth Nearly Ended 250 Million Years Ago, Princeton Univ. Press, 2006. |
[17] |
S. A. Frank, Dynamics of Cancer: Incidence, Inheritance and Evolution, Princeton University Press, 2007. |
[18] |
E. Gabetta and E. Regazzini, About the gene families size distribution in a recent model of genome evolution, Math. Models Methods Appl. Sci., 20 (2010), 1005-1020.
doi: 10.1142/S0218202510004519. |
[19] |
D. Hanahan and R.A. Weinberg, The hallmarks of cancer, Cell, 100 (2000), 57-70.
doi: 10.1016/S0092-8674(00)81683-9. |
[20] | |
[21] |
M. A Nowak and K. Sigmund, Evolutionary dynamics of biological games, Science, 303 (2004), 793-799.
doi: 10.1126/science.1093411. |
[22] |
M. A. Nowak, Evolutionary Dynamics. Exploring the Equations of Life, Harvard Univ. Press, 2006. |
[23] |
F. C. Santos, J. M. Pacheco and T. Lenaerts, Evolutionary dynamics of social dilemmas in structured heterogeneous populations, Proceeding of the National Academy of Sciences, 103 (2006), 3490-3494.
doi: 10.1073/pnas.0508201103. |
[24] |
F. C. Santos, V. V. Vasconcelos, M. D. Santos, P. N. B. Neves and J. M. Pacheco, Evolutionary dynamics of climate change under collective-risk dilemmas, Math. Models Methods Appl. Sci., 22 (2012), 1140004, 17 pp.
doi: 10.1142/S0218202511400045. |
[25] |
F. J. Weissing, Genetic versus phenotypic models of selection: Can genetics be neglected in a long-term perspective? J. Math. Biol., 34 (1996), 533-555.
doi: 10.1007/BF02409749. |
show all references
References:
[1] |
D. L. Abel and J. T. Trevors, Self-organization vs. self-ordering events in life-origin models, Physics of Life Reviews, 3 (2006), 221-228.
doi: 10.1016/j.plrev.2006.07.003. |
[2] |
G. Ajmone Marsan, N. Bellomo and M. Egidi, Towards a mathematical theory of complex socio-economical systems by functional subsystems reprsentation, Kinet. Relat. Models, 1 (2008), 249-278.
doi: 10.3934/krm.2008.1.249. |
[3] |
N. Bellomo and B. Carbonaro, Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives, Physics of Life Reviews, 8 (2011), 1-18.
doi: 10.1016/j.plrev.2010.12.001. |
[4] |
N. Bellomo, D. Knopoff and J. Soler, On the difficult interplay between life, "complexity,'' and mathematical sciences, Math. Models Methods Appl. Sci., 23 (2013), 1861-1913.
doi: 10.1142/S021820251350053X. |
[5] |
N. Bellomo, L. Preziosi and G. Forni, On a kinetic (cellular) theory for competition between tumors and the host immune system, J. Biological Systems, 4 (1996), 479-502.
doi: 10.1142/S0218339096000326. |
[6] |
N. Bellomo and J. Soler, On the mathematical theory of the dynamics of swarms viewed as complex systems, Math. Models Methods Appl. Sci., 22 (2012), suppl. 1, 1140006, 29 pp.
doi: 10.1142/S0218202511400069. |
[7] |
A. Belloquid and M. Delitala, Mathematical Modeling of Complex Biological Systems. A Kinetic Theory Approach, Birkhäuser, Boston, 2006.
doi: 10.1007/978-0-8176-4503-8. |
[8] |
A. Bellouquid, E. De Angelis and L. Fermo, Towards the modeling of vehicular traffic as a complex system: A kinetic theory approach, Math. Models Methods Appl. Sci., 22 (2012), suppl. 1, 1140003, 35 pp.
doi: 10.1142/S0218202511400033. |
[9] |
A. Bellouquid, E. De Angelis and D. Knopoff, From the modeling of the immune hallmarks of cancer to a black swan in biology, Math. Models Methods Appl. Sci., 23 (2013), 949-978.
doi: 10.1142/S0218202512500650. |
[10] |
E. L. Cooper, Evolution of immune system from self/not self to danger to artificial immune system (AIS), Physics of Life Reviews, 7 (2010), 55-78.
doi: 10.1016/j.plrev.2009.12.001. |
[11] |
M. Delitala, P. Pucci and M.C. Salvatori, From methods of the mathematical kinetic theory for active particles to modelling virus mutations, Math. Models Methods Appl. Sci., 21 (2011), suppl. 1, 843-870.
doi: 10.1142/S0218202511005398. |
[12] |
S. De Lillo, M. Delitala and M. C. Salvatori, Modelling epidemics and virus mutations by methods of the mathematical kinetic theory for active particles, Math. Models Methods Appl. Sci., 19 (2009), suppl. 1, 1405-1425.
doi: 10.1142/S0218202509003838. |
[13] |
K. Drucis, M. Kolev, W. Majda and B. Zubik-Kowal, Nonlinear modeling with mammographic evidence of carcinoma, Nonlinear Anal. Real World Appl., 11 (2010), 4326-4334.
doi: 10.1016/j.nonrwa.2010.05.017. |
[14] |
R. A. Gatenby and T. L. Vincent, An evolutionary model of carcinogenesis, Cancer Research, 63 (2003), 6212-6220. |
[15] |
R. A. Gatenby, T. L. Vincent and R. J. Gillies, Evolutionary dynamics in carcinogenesis, Math. Models Methods Appl. Sci., 15 (2005), 1619-1638.
doi: 10.1142/S0218202505000911. |
[16] |
D. H. Erwin, Extintion: How Life on Earth Nearly Ended 250 Million Years Ago, Princeton Univ. Press, 2006. |
[17] |
S. A. Frank, Dynamics of Cancer: Incidence, Inheritance and Evolution, Princeton University Press, 2007. |
[18] |
E. Gabetta and E. Regazzini, About the gene families size distribution in a recent model of genome evolution, Math. Models Methods Appl. Sci., 20 (2010), 1005-1020.
doi: 10.1142/S0218202510004519. |
[19] |
D. Hanahan and R.A. Weinberg, The hallmarks of cancer, Cell, 100 (2000), 57-70.
doi: 10.1016/S0092-8674(00)81683-9. |
[20] | |
[21] |
M. A Nowak and K. Sigmund, Evolutionary dynamics of biological games, Science, 303 (2004), 793-799.
doi: 10.1126/science.1093411. |
[22] |
M. A. Nowak, Evolutionary Dynamics. Exploring the Equations of Life, Harvard Univ. Press, 2006. |
[23] |
F. C. Santos, J. M. Pacheco and T. Lenaerts, Evolutionary dynamics of social dilemmas in structured heterogeneous populations, Proceeding of the National Academy of Sciences, 103 (2006), 3490-3494.
doi: 10.1073/pnas.0508201103. |
[24] |
F. C. Santos, V. V. Vasconcelos, M. D. Santos, P. N. B. Neves and J. M. Pacheco, Evolutionary dynamics of climate change under collective-risk dilemmas, Math. Models Methods Appl. Sci., 22 (2012), 1140004, 17 pp.
doi: 10.1142/S0218202511400045. |
[25] |
F. J. Weissing, Genetic versus phenotypic models of selection: Can genetics be neglected in a long-term perspective? J. Math. Biol., 34 (1996), 533-555.
doi: 10.1007/BF02409749. |
[1] |
Nicola Bellomo, Abdelghani Bellouquid, Juanjo Nieto, Juan Soler. Modeling chemotaxis from $L^2$--closure moments in kinetic theory of active particles. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 847-863. doi: 10.3934/dcdsb.2013.18.847 |
[2] |
Judith R. Miller, Huihui Zeng. Stability of traveling waves for systems of nonlinear integral recursions in spatial population biology. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 895-925. doi: 10.3934/dcdsb.2011.16.895 |
[3] |
Martin Parisot, Mirosław Lachowicz. A kinetic model for the formation of swarms with nonlinear interactions. Kinetic and Related Models, 2016, 9 (1) : 131-164. doi: 10.3934/krm.2016.9.131 |
[4] |
N. Bellomo, A. Bellouquid. From a class of kinetic models to the macroscopic equations for multicellular systems in biology. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 59-80. doi: 10.3934/dcdsb.2004.4.59 |
[5] |
Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic and Related Models, 2021, 14 (1) : 115-148. doi: 10.3934/krm.2020051 |
[6] |
Giuseppe Toscani, Andrea Tosin, Mattia Zanella. Kinetic modelling of multiple interactions in socio-economic systems. Networks and Heterogeneous Media, 2020, 15 (3) : 519-542. doi: 10.3934/nhm.2020029 |
[7] |
Nicolas Besse, Florent Berthelin, Yann Brenier, Pierre Bertrand. The multi-water-bag equations for collisionless kinetic modeling. Kinetic and Related Models, 2009, 2 (1) : 39-80. doi: 10.3934/krm.2009.2.39 |
[8] |
Mats Gyllenberg, Yi Wang. Periodic tridiagonal systems modeling competitive-cooperative ecological interactions. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 289-298. doi: 10.3934/dcdsb.2005.5.289 |
[9] |
Roberto Alicandro, Giuliano Lazzaroni, Mariapia Palombaro. Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours. Networks and Heterogeneous Media, 2018, 13 (1) : 1-26. doi: 10.3934/nhm.2018001 |
[10] |
Julian Braun, Bernd Schmidt. On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth. Networks and Heterogeneous Media, 2013, 8 (4) : 879-912. doi: 10.3934/nhm.2013.8.879 |
[11] |
Pierre Magal. Global stability for differential equations with homogeneous nonlinearity and application to population dynamics. Discrete and Continuous Dynamical Systems - B, 2002, 2 (4) : 541-560. doi: 10.3934/dcdsb.2002.2.541 |
[12] |
Michele Gianfelice, Enza Orlandi. Dynamics and kinetic limit for a system of noiseless $d$-dimensional Vicsek-type particles. Networks and Heterogeneous Media, 2014, 9 (2) : 269-297. doi: 10.3934/nhm.2014.9.269 |
[13] |
Eugene Kashdan, Dominique Duncan, Andrew Parnell, Heinz Schättler. Mathematical methods in systems biology. Mathematical Biosciences & Engineering, 2016, 13 (6) : i-ii. doi: 10.3934/mbe.201606i |
[14] |
Daewa Kim, Annalisa Quaini. A kinetic theory approach to model pedestrian dynamics in bounded domains with obstacles. Kinetic and Related Models, 2019, 12 (6) : 1273-1296. doi: 10.3934/krm.2019049 |
[15] |
Jean-Philippe Bernard, Emmanuel Frénod, Antoine Rousseau. Modeling confinement in Étang de Thau: Numerical simulations and multi-scale aspects. Conference Publications, 2013, 2013 (special) : 69-76. doi: 10.3934/proc.2013.2013.69 |
[16] |
Mauro Maggioni, James M. Murphy. Learning by active nonlinear diffusion. Foundations of Data Science, 2019, 1 (3) : 271-291. doi: 10.3934/fods.2019012 |
[17] |
Nicolas Forcadel, Cyril Imbert, Régis Monneau. Homogenization of some particle systems with two-body interactions and of the dislocation dynamics. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 785-826. doi: 10.3934/dcds.2009.23.785 |
[18] |
Sarbaz H. A. Khoshnaw. Reduction of a kinetic model of active export of importins. Conference Publications, 2015, 2015 (special) : 705-722. doi: 10.3934/proc.2015.0705 |
[19] |
Robert A. Gatenby, B. Roy Frieden. The Role of Non-Genomic Information in Maintaining Thermodynamic Stability in Living Systems. Mathematical Biosciences & Engineering, 2005, 2 (1) : 43-51. doi: 10.3934/mbe.2005.2.43 |
[20] |
MirosŁaw Lachowicz, Tatiana Ryabukha. Equilibrium solutions for microscopic stochastic systems in population dynamics. Mathematical Biosciences & Engineering, 2013, 10 (3) : 777-786. doi: 10.3934/mbe.2013.10.777 |
2021 Impact Factor: 1.865
Tools
Metrics
Other articles
by authors
[Back to Top]