September  2015, 10(3): 421-441. doi: 10.3934/nhm.2015.10.421

From a systems theory of sociology to modeling the onset and evolution of criminality

1. 

Department of Mathematics, Faculty Sciences, King Abdulaziz University, Jeddah, Saudi Arabia

2. 

Department of Mathematical Sciences, Politecnico of Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

3. 

Centro de Investigación y Estudios de Matemática (CONICET), Medina Allende s/n, 5000 Córdoba, Argentina

4. 

Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada

Received  October 2014 Revised  January 2015 Published  July 2015

This paper proposes a systems theory approach to the modeling of onset and evolution of criminality in a territory. This approach aims at capturing the complexity features of social systems. Complexity is related to the fact that individuals have the ability to develop specific heterogeneously distributed strategies, which depend also on those expressed by the other individuals. The modeling is developed by methods of generalized kinetic theory where interactions and decisional processes are modeled by theoretical tools of stochastic game theory.
Citation: Nicola Bellomo, Francesca Colasuonno, Damián Knopoff, Juan Soler. From a systems theory of sociology to modeling the onset and evolution of criminality. Networks and Heterogeneous Media, 2015, 10 (3) : 421-441. doi: 10.3934/nhm.2015.10.421
References:
[1]

G. Ajmone Marsan, N. Bellomo and M. Egidi, Towards a mathematical theory of complex socio-economical systems by functional subsystems representation, Kinet. Relat. Models, 1 (2008), 249-278. doi: 10.3934/krm.2008.1.249.

[2]

L. Arlotti, E. De Angelis, L. Fermo, M. Lachowicz and N. Bellomo, On a class of integro-differential equations modeling complex systems with nonlinear interactions, Appl. Math. Lett., 25 (2012), 490-495. doi: 10.1016/j.aml.2011.09.043.

[3]

W. B. Arthur, S. N. Durlauf and D. A. Lane, Eds., The Economy as an Evolving Complex System II, Studies in the Sciences of Complexity, XXVII, Addison-Wesley, 1997.

[4]

K. D. Baily, Sociology and the New System Theory - Towards a Theoretical Synthesis, Suny Press, 1994.

[5]

P. Ball, Why Society is a Complex Matter: Meeting Twenty-first Century Challenges with a New Kind of Science, Springer-Verlag, Heidelberg, 2012. doi: 10.1007/978-3-642-29000-8.

[6]

M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proc. Natl. Acad. Sci. USA, 105 (2008), 1232-1237. doi: 10.1073/pnas.0711437105.

[7]

N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, Multicellular biological growing systems: Hyperbolic limits towards macroscopic description, Math. Models Methods Appl. Sci., 17 (2007), 1675-1692. doi: 10.1142/S0218202507002431.

[8]

N. Bellomo, M. A. Herrero and A. Tosin, On the dynamics of social conflicts: Looking for the Black Swan, Kinet. Relat. Mod., 6 (2013), 459-479. doi: 10.3934/krm.2013.6.459.

[9]

N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system viewpoint, Math. Models Methods Appl. Sci., 22 (2012), paper No.1230004. doi: 10.1142/S0218202512300049.

[10]

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), paper No.1140006. doi: 10.1142/S0218202511400069.

[11]

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.

[12]

N. Bellomo and M. Pulvirenti, Eds., Modeling in Applied Sciences - A Kinetic Theory Approach, Birkhäuser, Boston, 2000. doi: 10.1007/978-1-4612-0513-5.

[13]

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.

[14]

B. Berenji, T. Chou and M. D'Orsogna, Recidivism and rehabilitation of criminal offenders: A carrot and stick evolutionary games, PLOS ONE, 9 (2014), 885531. doi: 10.1371/journal.pone.0085531.

[15]

H. Berestycki, J. Wei and M. Winter, Existence of symmetric and asymmetric spikes of a crime hotspot model, SAM J. Math. Anal., 46 (2014), 691-719. doi: 10.1137/130922744.

[16]

L. M. A. Bettencourt, J. Lobo, D. Helbing, C. Kohnert and G. B. West, Growth, innovation, scaling, and the pace of life in cities, Proc. Natl. Acad. Sci. USA, 104 (2007), 7301-7306. doi: 10.1073/pnas.0610172104.

[17]

J. J. Bissell, C. C. S. Caiado, M. Goldstein and B. Straughan, Compartmental modelling of social dynamics with generalized peer incidence, Math. Models Methods Appl. Sci., 24 (2014), 719-750. doi: 10.1142/S0218202513500656.

[18]

F. Colasuonno and M. C. Salvatori, Existence and uniqueness of solutions to a Cauchy problem modeling the dynamics of socio-political conflicts, in Recent Trends in Nonlinear Partial Differential Equations I: Evolution Problems (eds. J. B. Serrin, E. L. Mitidieri and V. D. Radulescu), Series Cont. Math. AMS, Providence, USA, Contemporary Mathematics, 594 (2013), 155-165. doi: 10.1090/conm/594/11789.

[19]

T. Davies, H. Fry, A. Wilson and S. Bishop, A Mathematical Model of the London Riots and Their Policing, Scientific Report, 2013. doi: 10.1038/srep01303.

[20]

E. De Angelis, On the mathematical theory of post-Darwinian mutations, selection, and evolution, Math. Models Methods Appl. Sci., 24 (2014), 2723-2742. doi: 10.1142/S0218202514500353.

[21]

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), 1405-1425. doi: 10.1142/S0218202509003838.

[22]

M. Dolfin and M. Lachowicz, Modeling altruism and selfishness in welfare dynamics: The role of nonlinear interactions, Math. Models Methods Appl. Sci., 24 (2014), 2361-2381. doi: 10.1142/S0218202514500237.

[23]

M. D'Orsogna, R. Kendall, M. McBride and M. B. Short, Criminal defectors lead to the emergence of cooperation in an experimental,adversarial game, PLOS ONE, 8 (2013), e61458. doi: 10.1371/journal.pone.0061458.

[24]

M. D'Orsogna and M. Perc, Statistical physics of crime: A review, Phys. Life Rev., 12 (2014), 1-21.

[25]

B. Düring, P. Markowich, J.-F. Pietschmann and M.-T. Wolfram, Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders, P. R. Soc. London, 465 (2009), 3687-3708. doi: 10.1098/rspa.2009.0239.

[26]

P. Fajnzlber, D. Lederman and N. Loayza, Inequality and violent crime, J. Law Econ., 45 (2002), 1-39. doi: 10.1086/338347.

[27]

M. Felson, What every mathematician should know about modelling crime, Eur. J. Appl. Math., 21 (2010), 275-281. doi: 10.1017/S0956792510000070.

[28]

S. Harrendorf, M. Heiskanen and S. Malby, International Statistics on Crime and Justice, European Institute for Crime Prevention and Control, affiliated with the United Nations (HEUNI), 2010.

[29]

D. Helbing, Quantitative Sociodynamics. Stochastic Methods and Models of Social Interaction Processes, 2nd edition, Springer, Berlin Heidelberg, 2010. doi: 10.1007/978-3-642-11546-2.

[30]

C. C. Hsieh and M. D. Pugh, Poverty, income inequality, and violent crime: A meta-analysis of recent aggregate data studies, Crim. Just. Rev., 18 (1993), 182-202. doi: 10.1177/073401689301800203.

[31]

E. Jager and L. Segel, On the distribution of dominance in populations of social organisms, SIAM J. Appl. Math., 52 (1992), 1442-1468. doi: 10.1137/0152083.

[32]

A. P. Kirman and N. J. Vriend, Learning to be loyal. A study of the Marseille fish market, in Interaction and Market Structure, Lecture Notes in Economics and Mathematical Systems, 484, Springer-Verlag, Heidelberg, 2000, 33-56. doi: 10.1007/978-3-642-57005-6_3.

[33]

D. Knopoff, On the modeling of migration phenomena on small networks, Math. Models Methods Appl. Sci., 23 (2013), 541-563. doi: 10.1142/S0218202512500558.

[34]

D. Knopoff, On a mathematical theory of complex systems on networks with application to opinion formation, Math. Models Methods Appl. Sci., 24 (2014), 405-426. doi: 10.1142/S0218202513400137.

[35]

R. M. May, Uses and abuses of mathematics in biology, Science, 303 (2004), 790-793. doi: 10.1126/science.1094442.

[36]

S. McCalla, M. Short and P. J. Brantingham, The effects of sacred value networks within and evolutionary, adversarial game, J. Stat. Phys., 151 (2013), 673-688. doi: 10.1007/s10955-012-0678-4.

[37]

G. Mohler and M. Short, Geographic profiling form kinetic models of criminal behavior, SIAM J. Appl. Math., 72 (2012), 163-180. doi: 10.1137/100794080.

[38]

M. A. Nowak, Evolutionary Dynamics. Exploring the Equations of Life, Harvard University Press, 2006.

[39]

J. C. Nuño, M. A. Herrero and M. Primicerio, A mathematical model of a criminal-prone society, Discr. Cont. Dyn. Syst. S, 4 (2011), 193-207. doi: 10.3934/dcdss.2011.4.193.

[40]

H. Othmer, S. R. Dunbar and W. Alt, Models of dispersal in biological systems, J. Math. Biol., 26 (1988), 263-298. doi: 10.1007/BF00277392.

[41]

P. Ormerod, Crime: Economic incentives and social networks, IEA Hobart Paper, 151 (2005), 1-54. doi: 10.2139/ssrn.879716.

[42]

L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, Oxford University Press, USA, 2013.

[43]

P. Pucci and M. C. Salvatori, On an initial value problem modeling evolution and selection in living systems, Disc. Cont. Dyn. Syst. S, 7 (2014), 807-821. doi: 10.3934/dcdss.2014.7.807.

[44]

M. B. Short, P. J. Brantingham and M. R. D'Orsogna, Cooperation and punishment in an adversarial game: How defectors pave the way to a peaceful society, Phys. Rev. E, 82 (2010), 066114, 7pp. doi: 10.1103/PhysRevE.82.066114.

[45]

M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci., 18 (2008), 1249-1267. doi: 10.1142/S0218202508003029.

[46]

H. A. Simon, Models of Bounded Rationality: Empirically Grounded Economic Reason, Volume 3, MIT Press, Cambridge, MA, 1997.

[47]

P. E. Tetlock, Thinking the unthinkable: Sacred values and taboo cognitions, Trends Cogn. Sci., 7 (2003), 320-324. doi: 10.1016/S1364-6613(03)00135-9.

show all references

References:
[1]

G. Ajmone Marsan, N. Bellomo and M. Egidi, Towards a mathematical theory of complex socio-economical systems by functional subsystems representation, Kinet. Relat. Models, 1 (2008), 249-278. doi: 10.3934/krm.2008.1.249.

[2]

L. Arlotti, E. De Angelis, L. Fermo, M. Lachowicz and N. Bellomo, On a class of integro-differential equations modeling complex systems with nonlinear interactions, Appl. Math. Lett., 25 (2012), 490-495. doi: 10.1016/j.aml.2011.09.043.

[3]

W. B. Arthur, S. N. Durlauf and D. A. Lane, Eds., The Economy as an Evolving Complex System II, Studies in the Sciences of Complexity, XXVII, Addison-Wesley, 1997.

[4]

K. D. Baily, Sociology and the New System Theory - Towards a Theoretical Synthesis, Suny Press, 1994.

[5]

P. Ball, Why Society is a Complex Matter: Meeting Twenty-first Century Challenges with a New Kind of Science, Springer-Verlag, Heidelberg, 2012. doi: 10.1007/978-3-642-29000-8.

[6]

M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proc. Natl. Acad. Sci. USA, 105 (2008), 1232-1237. doi: 10.1073/pnas.0711437105.

[7]

N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, Multicellular biological growing systems: Hyperbolic limits towards macroscopic description, Math. Models Methods Appl. Sci., 17 (2007), 1675-1692. doi: 10.1142/S0218202507002431.

[8]

N. Bellomo, M. A. Herrero and A. Tosin, On the dynamics of social conflicts: Looking for the Black Swan, Kinet. Relat. Mod., 6 (2013), 459-479. doi: 10.3934/krm.2013.6.459.

[9]

N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system viewpoint, Math. Models Methods Appl. Sci., 22 (2012), paper No.1230004. doi: 10.1142/S0218202512300049.

[10]

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), paper No.1140006. doi: 10.1142/S0218202511400069.

[11]

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.

[12]

N. Bellomo and M. Pulvirenti, Eds., Modeling in Applied Sciences - A Kinetic Theory Approach, Birkhäuser, Boston, 2000. doi: 10.1007/978-1-4612-0513-5.

[13]

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.

[14]

B. Berenji, T. Chou and M. D'Orsogna, Recidivism and rehabilitation of criminal offenders: A carrot and stick evolutionary games, PLOS ONE, 9 (2014), 885531. doi: 10.1371/journal.pone.0085531.

[15]

H. Berestycki, J. Wei and M. Winter, Existence of symmetric and asymmetric spikes of a crime hotspot model, SAM J. Math. Anal., 46 (2014), 691-719. doi: 10.1137/130922744.

[16]

L. M. A. Bettencourt, J. Lobo, D. Helbing, C. Kohnert and G. B. West, Growth, innovation, scaling, and the pace of life in cities, Proc. Natl. Acad. Sci. USA, 104 (2007), 7301-7306. doi: 10.1073/pnas.0610172104.

[17]

J. J. Bissell, C. C. S. Caiado, M. Goldstein and B. Straughan, Compartmental modelling of social dynamics with generalized peer incidence, Math. Models Methods Appl. Sci., 24 (2014), 719-750. doi: 10.1142/S0218202513500656.

[18]

F. Colasuonno and M. C. Salvatori, Existence and uniqueness of solutions to a Cauchy problem modeling the dynamics of socio-political conflicts, in Recent Trends in Nonlinear Partial Differential Equations I: Evolution Problems (eds. J. B. Serrin, E. L. Mitidieri and V. D. Radulescu), Series Cont. Math. AMS, Providence, USA, Contemporary Mathematics, 594 (2013), 155-165. doi: 10.1090/conm/594/11789.

[19]

T. Davies, H. Fry, A. Wilson and S. Bishop, A Mathematical Model of the London Riots and Their Policing, Scientific Report, 2013. doi: 10.1038/srep01303.

[20]

E. De Angelis, On the mathematical theory of post-Darwinian mutations, selection, and evolution, Math. Models Methods Appl. Sci., 24 (2014), 2723-2742. doi: 10.1142/S0218202514500353.

[21]

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), 1405-1425. doi: 10.1142/S0218202509003838.

[22]

M. Dolfin and M. Lachowicz, Modeling altruism and selfishness in welfare dynamics: The role of nonlinear interactions, Math. Models Methods Appl. Sci., 24 (2014), 2361-2381. doi: 10.1142/S0218202514500237.

[23]

M. D'Orsogna, R. Kendall, M. McBride and M. B. Short, Criminal defectors lead to the emergence of cooperation in an experimental,adversarial game, PLOS ONE, 8 (2013), e61458. doi: 10.1371/journal.pone.0061458.

[24]

M. D'Orsogna and M. Perc, Statistical physics of crime: A review, Phys. Life Rev., 12 (2014), 1-21.

[25]

B. Düring, P. Markowich, J.-F. Pietschmann and M.-T. Wolfram, Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders, P. R. Soc. London, 465 (2009), 3687-3708. doi: 10.1098/rspa.2009.0239.

[26]

P. Fajnzlber, D. Lederman and N. Loayza, Inequality and violent crime, J. Law Econ., 45 (2002), 1-39. doi: 10.1086/338347.

[27]

M. Felson, What every mathematician should know about modelling crime, Eur. J. Appl. Math., 21 (2010), 275-281. doi: 10.1017/S0956792510000070.

[28]

S. Harrendorf, M. Heiskanen and S. Malby, International Statistics on Crime and Justice, European Institute for Crime Prevention and Control, affiliated with the United Nations (HEUNI), 2010.

[29]

D. Helbing, Quantitative Sociodynamics. Stochastic Methods and Models of Social Interaction Processes, 2nd edition, Springer, Berlin Heidelberg, 2010. doi: 10.1007/978-3-642-11546-2.

[30]

C. C. Hsieh and M. D. Pugh, Poverty, income inequality, and violent crime: A meta-analysis of recent aggregate data studies, Crim. Just. Rev., 18 (1993), 182-202. doi: 10.1177/073401689301800203.

[31]

E. Jager and L. Segel, On the distribution of dominance in populations of social organisms, SIAM J. Appl. Math., 52 (1992), 1442-1468. doi: 10.1137/0152083.

[32]

A. P. Kirman and N. J. Vriend, Learning to be loyal. A study of the Marseille fish market, in Interaction and Market Structure, Lecture Notes in Economics and Mathematical Systems, 484, Springer-Verlag, Heidelberg, 2000, 33-56. doi: 10.1007/978-3-642-57005-6_3.

[33]

D. Knopoff, On the modeling of migration phenomena on small networks, Math. Models Methods Appl. Sci., 23 (2013), 541-563. doi: 10.1142/S0218202512500558.

[34]

D. Knopoff, On a mathematical theory of complex systems on networks with application to opinion formation, Math. Models Methods Appl. Sci., 24 (2014), 405-426. doi: 10.1142/S0218202513400137.

[35]

R. M. May, Uses and abuses of mathematics in biology, Science, 303 (2004), 790-793. doi: 10.1126/science.1094442.

[36]

S. McCalla, M. Short and P. J. Brantingham, The effects of sacred value networks within and evolutionary, adversarial game, J. Stat. Phys., 151 (2013), 673-688. doi: 10.1007/s10955-012-0678-4.

[37]

G. Mohler and M. Short, Geographic profiling form kinetic models of criminal behavior, SIAM J. Appl. Math., 72 (2012), 163-180. doi: 10.1137/100794080.

[38]

M. A. Nowak, Evolutionary Dynamics. Exploring the Equations of Life, Harvard University Press, 2006.

[39]

J. C. Nuño, M. A. Herrero and M. Primicerio, A mathematical model of a criminal-prone society, Discr. Cont. Dyn. Syst. S, 4 (2011), 193-207. doi: 10.3934/dcdss.2011.4.193.

[40]

H. Othmer, S. R. Dunbar and W. Alt, Models of dispersal in biological systems, J. Math. Biol., 26 (1988), 263-298. doi: 10.1007/BF00277392.

[41]

P. Ormerod, Crime: Economic incentives and social networks, IEA Hobart Paper, 151 (2005), 1-54. doi: 10.2139/ssrn.879716.

[42]

L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, Oxford University Press, USA, 2013.

[43]

P. Pucci and M. C. Salvatori, On an initial value problem modeling evolution and selection in living systems, Disc. Cont. Dyn. Syst. S, 7 (2014), 807-821. doi: 10.3934/dcdss.2014.7.807.

[44]

M. B. Short, P. J. Brantingham and M. R. D'Orsogna, Cooperation and punishment in an adversarial game: How defectors pave the way to a peaceful society, Phys. Rev. E, 82 (2010), 066114, 7pp. doi: 10.1103/PhysRevE.82.066114.

[45]

M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci., 18 (2008), 1249-1267. doi: 10.1142/S0218202508003029.

[46]

H. A. Simon, Models of Bounded Rationality: Empirically Grounded Economic Reason, Volume 3, MIT Press, Cambridge, MA, 1997.

[47]

P. E. Tetlock, Thinking the unthinkable: Sacred values and taboo cognitions, Trends Cogn. Sci., 7 (2003), 320-324. doi: 10.1016/S1364-6613(03)00135-9.

[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]

Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci. Collisionless kinetic theory of rolling molecules. Kinetic and Related Models, 2013, 6 (2) : 429-458. doi: 10.3934/krm.2013.6.429

[3]

Emmanuel Frénod, Mathieu Lutz. On the Geometrical Gyro-Kinetic theory. Kinetic and Related Models, 2014, 7 (4) : 621-659. doi: 10.3934/krm.2014.7.621

[4]

Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics and Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013

[5]

Leon Petrosyan, David Yeung. Shapley value for differential network games: Theory and application. Journal of Dynamics and Games, 2021, 8 (2) : 151-166. doi: 10.3934/jdg.2020021

[6]

Etienne Bernard, Laurent Desvillettes, Franç cois Golse, Valeria Ricci. A derivation of the Vlasov-Stokes system for aerosol flows from the kinetic theory of binary gas mixtures. Kinetic and Related Models, 2018, 11 (1) : 43-69. doi: 10.3934/krm.2018003

[7]

Serap Ergün, Bariş Bülent Kırlar, Sırma Zeynep Alparslan Gök, Gerhard-Wilhelm Weber. An application of crypto cloud computing in social networks by cooperative game theory. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1927-1941. doi: 10.3934/jimo.2019036

[8]

Zhaoyang Qiu, Yixuan Wang. Martingale solution for stochastic active liquid crystal system. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2227-2268. doi: 10.3934/dcds.2020360

[9]

Paolo Barbante, Aldo Frezzotti, Livio Gibelli. A kinetic theory description of liquid menisci at the microscale. Kinetic and Related Models, 2015, 8 (2) : 235-254. doi: 10.3934/krm.2015.8.235

[10]

Hung-Wen Kuo. Effect of abrupt change of the wall temperature in the kinetic theory. Kinetic and Related Models, 2019, 12 (4) : 765-789. doi: 10.3934/krm.2019030

[11]

José Antonio Alcántara, Simone Calogero. On a relativistic Fokker-Planck equation in kinetic theory. Kinetic and Related Models, 2011, 4 (2) : 401-426. doi: 10.3934/krm.2011.4.401

[12]

Krešimir Burazin, Marko Vrdoljak. Homogenisation theory for Friedrichs systems. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1017-1044. doi: 10.3934/cpaa.2014.13.1017

[13]

Manfred Deistler. Singular arma systems: A structure theory. Numerical Algebra, Control and Optimization, 2019, 9 (3) : 383-391. doi: 10.3934/naco.2019025

[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]

José A. Carrillo, M. R. D’Orsogna, V. Panferov. Double milling in self-propelled swarms from kinetic theory. Kinetic and Related Models, 2009, 2 (2) : 363-378. doi: 10.3934/krm.2009.2.363

[16]

Marzia Bisi, Tommaso Ruggeri, Giampiero Spiga. Dynamical pressure in a polyatomic gas: Interplay between kinetic theory and extended thermodynamics. Kinetic and Related Models, 2018, 11 (1) : 71-95. doi: 10.3934/krm.2018004

[17]

Carlos Escudero, Fabricio Macià, Raúl Toral, Juan J. L. Velázquez. Kinetic theory and numerical simulations of two-species coagulation. Kinetic and Related Models, 2014, 7 (2) : 253-290. doi: 10.3934/krm.2014.7.253

[18]

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

[19]

Jérôme Coville, Juan Dávila. Existence of radial stationary solutions for a system in combustion theory. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 739-766. doi: 10.3934/dcdsb.2011.16.739

[20]

Pierre Degond, Simone Goettlich, Axel Klar, Mohammed Seaid, Andreas Unterreiter. Derivation of a kinetic model from a stochastic particle system. Kinetic and Related Models, 2008, 1 (4) : 557-572. doi: 10.3934/krm.2008.1.557

2020 Impact Factor: 1.213

Metrics

  • PDF downloads (126)
  • HTML views (0)
  • Cited by (13)

[Back to Top]