September  2013, 6(3): 459-479. doi: 10.3934/krm.2013.6.459

On the dynamics of social conflicts: Looking for the black swan

1. 

Department of Mathematica Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino

2. 

Department of Applied Mathematics, Universidad Complutense, Plaza de Ciencias 3, Ciudad Universitaria, 28040 Madrid, Spain

3. 

Istituto per le Applicazioni del Calcolo "M. Picone", Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Roma, Italy

Received  January 2013 Revised  January 2013 Published  May 2013

This paper deals with the modeling of social competition, possibly resulting in the onset of extreme conflicts. More precisely, we discuss models describing the interplay between individual competition for wealth distribution that, when coupled with political stances coming from support or opposition to a Government, may give rise to strongly self-enhanced effects. The latter may be thought of as the early stages of massive unpredictable events known as Black Swans, although no analysis of any fully-developed Black Swan is provided here. Our approach makes use of the framework of the kinetic theory for active particles, where nonlinear interactions among subjects are modeled according to game-theoretical principles.
Citation: Nicola Bellomo, Miguel A. Herrero, Andrea Tosin. On the dynamics of social conflicts: Looking for the black swan. Kinetic & Related Models, 2013, 6 (3) : 459-479. doi: 10.3934/krm.2013.6.459
References:
[1]

Studies in the Sciences of Complexity, Vol. XXVII, Addison-Wesley, 1997. Google Scholar

[2]

Cambridge University Press, 2005. doi: 10.1017/CBO9780511510809.  Google Scholar

[3]

J. Eur. Econ. Assoc., 9 (2011), 177-208. Google Scholar

[4]

Kinet. Relat. Models, 1 (2008), 249-278. doi: 10.3934/krm.2008.1.249.  Google Scholar

[5]

Comput. Math. Appl., 57 (2009), 710-728. doi: 10.1016/j.camwa.2008.09.003.  Google Scholar

[6]

J. Public Econ., 89 (2005), 1333-1354. Google Scholar

[7]

Appl. Math. Lett., 9 (1996), 65-70. doi: 10.1016/0893-9659(96)00014-6.  Google Scholar

[8]

Math. Models Methods Appl. Sci., 12 (2002), 567-591. doi: 10.1142/S0218202502001799.  Google Scholar

[9]

Appl. Math. Lett., 25 (2012), 490-495. doi: 10.1016/j.aml.2011.09.043.  Google Scholar

[10]

Proc. Natl. Acad. Sci. USA, 105 (2008), 1232-1237. doi: 10.1073/pnas.0711437105.  Google Scholar

[11]

Physica A, 272 (1999), 173-187. Google Scholar

[12]

Nature, 458 (2009), 1018-1020. doi: 10.1038/nature07950.  Google Scholar

[13]

Math. Models Methods Appl. Sci., 22 (2012), 1140006, 29 pp. doi: 10.1142/S0218202511400069.  Google Scholar

[14]

Math. Models Methods Appl. Sci., 22 (2012), 1140003, 35 pp. doi: 10.1142/S0218202511400033.  Google Scholar

[15]

Nonlinear Anal. Real World Appl., 9 (2008), 183-196. doi: 10.1016/j.nonrwa.2006.09.012.  Google Scholar

[16]

Math. Comput. Modelling, 48 (2008), 1107-1121. doi: 10.1016/j.mcm.2007.12.021.  Google Scholar

[17]

Princeton University Press, 2003. Google Scholar

[18]

Comput. Math. Appl., 62 (2011), 3902-3911. doi: 10.1016/j.camwa.2011.09.043.  Google Scholar

[19]

J. Math. Biol., 62 (2011), 569-588. doi: 10.1007/s00285-010-0347-7.  Google Scholar

[20]

Math. Models Methods Appl. Sci., 21 (2011), 843-870. doi: 10.1142/S0218202511005398.  Google Scholar

[21]

P. R. Soc. London Ser. A Math. Phys. Eng. Sci., 465 (2009), 3687-3708. doi: 10.1098/rspa.2009.0239.  Google Scholar

[22]

Second edition, Springer, Heidelberg, 2010. doi: 10.1007/978-3-642-11546-2.  Google Scholar

[23]

Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), 193-207. doi: 10.3934/dcdss.2011.4.193.  Google Scholar

[24]

Proc. Natl. Acad. Sci. USA, 108 (2011), 19193-19198. Google Scholar

[25]

Nature, 461 (2009), 53-59. doi: 10.1038/nature08227.  Google Scholar

[26]

Am. Econ. Rev., 49 (1959), 253-283. Google Scholar

[27]

Vol. 1, MIT Press, Cambridge, MA, 1982. Google Scholar

[28]

Vol. 3, MIT Press, Cambridge, MA, 1997. Google Scholar

[29]

Random House, New York City, 2007. Google Scholar

[30]

Commun. Math. Sci., 4 (2006), 481-496.  Google Scholar

[31]

Econometric Society Monographs, 44, Cambridge University Press, Cambridge, 2007.  Google Scholar

[32]

Monographs and Textbooks in Pure and Applied Mathematics, 89, Marcel Dekker, Inc., New York, 1985.  Google Scholar

show all references

References:
[1]

Studies in the Sciences of Complexity, Vol. XXVII, Addison-Wesley, 1997. Google Scholar

[2]

Cambridge University Press, 2005. doi: 10.1017/CBO9780511510809.  Google Scholar

[3]

J. Eur. Econ. Assoc., 9 (2011), 177-208. Google Scholar

[4]

Kinet. Relat. Models, 1 (2008), 249-278. doi: 10.3934/krm.2008.1.249.  Google Scholar

[5]

Comput. Math. Appl., 57 (2009), 710-728. doi: 10.1016/j.camwa.2008.09.003.  Google Scholar

[6]

J. Public Econ., 89 (2005), 1333-1354. Google Scholar

[7]

Appl. Math. Lett., 9 (1996), 65-70. doi: 10.1016/0893-9659(96)00014-6.  Google Scholar

[8]

Math. Models Methods Appl. Sci., 12 (2002), 567-591. doi: 10.1142/S0218202502001799.  Google Scholar

[9]

Appl. Math. Lett., 25 (2012), 490-495. doi: 10.1016/j.aml.2011.09.043.  Google Scholar

[10]

Proc. Natl. Acad. Sci. USA, 105 (2008), 1232-1237. doi: 10.1073/pnas.0711437105.  Google Scholar

[11]

Physica A, 272 (1999), 173-187. Google Scholar

[12]

Nature, 458 (2009), 1018-1020. doi: 10.1038/nature07950.  Google Scholar

[13]

Math. Models Methods Appl. Sci., 22 (2012), 1140006, 29 pp. doi: 10.1142/S0218202511400069.  Google Scholar

[14]

Math. Models Methods Appl. Sci., 22 (2012), 1140003, 35 pp. doi: 10.1142/S0218202511400033.  Google Scholar

[15]

Nonlinear Anal. Real World Appl., 9 (2008), 183-196. doi: 10.1016/j.nonrwa.2006.09.012.  Google Scholar

[16]

Math. Comput. Modelling, 48 (2008), 1107-1121. doi: 10.1016/j.mcm.2007.12.021.  Google Scholar

[17]

Princeton University Press, 2003. Google Scholar

[18]

Comput. Math. Appl., 62 (2011), 3902-3911. doi: 10.1016/j.camwa.2011.09.043.  Google Scholar

[19]

J. Math. Biol., 62 (2011), 569-588. doi: 10.1007/s00285-010-0347-7.  Google Scholar

[20]

Math. Models Methods Appl. Sci., 21 (2011), 843-870. doi: 10.1142/S0218202511005398.  Google Scholar

[21]

P. R. Soc. London Ser. A Math. Phys. Eng. Sci., 465 (2009), 3687-3708. doi: 10.1098/rspa.2009.0239.  Google Scholar

[22]

Second edition, Springer, Heidelberg, 2010. doi: 10.1007/978-3-642-11546-2.  Google Scholar

[23]

Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), 193-207. doi: 10.3934/dcdss.2011.4.193.  Google Scholar

[24]

Proc. Natl. Acad. Sci. USA, 108 (2011), 19193-19198. Google Scholar

[25]

Nature, 461 (2009), 53-59. doi: 10.1038/nature08227.  Google Scholar

[26]

Am. Econ. Rev., 49 (1959), 253-283. Google Scholar

[27]

Vol. 1, MIT Press, Cambridge, MA, 1982. Google Scholar

[28]

Vol. 3, MIT Press, Cambridge, MA, 1997. Google Scholar

[29]

Random House, New York City, 2007. Google Scholar

[30]

Commun. Math. Sci., 4 (2006), 481-496.  Google Scholar

[31]

Econometric Society Monographs, 44, Cambridge University Press, Cambridge, 2007.  Google Scholar

[32]

Monographs and Textbooks in Pure and Applied Mathematics, 89, Marcel Dekker, Inc., New York, 1985.  Google Scholar

[1]

Jun Moon. Linear-quadratic mean-field type stackelberg differential games for stochastic jump-diffusion systems. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021026

[2]

Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329

[3]

Wenjuan Zhao, Shunfu Jin, Wuyi Yue. A stochastic model and social optimization of a blockchain system based on a general limited batch service queue. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1845-1861. doi: 10.3934/jimo.2020049

[4]

Dayalal Suthar, Sunil Dutt Purohit, Haile Habenom, Jagdev Singh. Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021019

[5]

Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451

[6]

Jamal Mrazgua, El Houssaine Tissir, Mohamed Ouahi. Frequency domain $ H_{\infty} $ control design for active suspension systems. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021036

[7]

Qi Lü, Xu Zhang. A concise introduction to control theory for stochastic partial differential equations. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021020

[8]

Zhaoqiang Ge. Controllability and observability of stochastic implicit systems and stochastic GE-evolution operator. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021009

[9]

Zhang Chen, Xiliang Li, Bixiang Wang. Invariant measures of stochastic delay lattice systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3235-3269. doi: 10.3934/dcdsb.2020226

[10]

Jicheng Liu, Meiling Zhao. Normal deviation of synchronization of stochastic coupled systems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021079

[11]

John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021004

[12]

Rabiaa Ouahabi, Nasr-Eddine Hamri. Design of new scheme adaptive generalized hybrid projective synchronization for two different chaotic systems with uncertain parameters. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2361-2370. doi: 10.3934/dcdsb.2020182

[13]

Xiongxiong Bao, Wan-Tong Li. Existence and stability of generalized transition waves for time-dependent reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3621-3641. doi: 10.3934/dcdsb.2020249

[14]

İsmail Özcan, Sirma Zeynep Alparslan Gök. On cooperative fuzzy bubbly games. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021010

[15]

Pengfei Wang, Mengyi Zhang, Huan Su. Input-to-state stability of infinite-dimensional stochastic nonlinear systems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021066

[16]

Kamel Hamdache, Djamila Hamroun. Macroscopic limit of the kinetic Bloch equation. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021015

[17]

Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang, Xingyong Li. Complexity in time-delay networks of multiple interacting neural groups. Electronic Research Archive, , () : -. doi: 10.3934/era.2021022

[18]

Longxiang Fang, Narayanaswamy Balakrishnan, Wenyu Huang. Stochastic comparisons of parallel systems with scale proportional hazards components equipped with starting devices. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021004

[19]

Fuzhi Li, Dongmei Xu. Regular dynamics for stochastic Fitzhugh-Nagumo systems with additive noise on thin domains. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3517-3542. doi: 10.3934/dcdsb.2020244

[20]

Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006

2019 Impact Factor: 1.311

Metrics

  • PDF downloads (174)
  • HTML views (0)
  • Cited by (65)

Other articles
by authors

[Back to Top]