Towards a mathematical theory of complex socio-economical systems by functional subsystems representation

Previous Article
Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models
KRM Home
This Issue
Next Article
Modelling and simulation of vehicular traffic jam formation

2008, 1(2): 249-278. doi: 10.3934/krm.2008.1.249

Towards a mathematical theory of complex socio-economical systems by functional subsystems representation

Giulia Ajmone Marsan ^1, , Nicola Bellomo ^2, and Massimo Egidi ^3,

1.	IMT -Institute for Advanced Studies Lucca, Piazza San Ponziano 6, 55100 Lucca, Italy
2.	Department of Mathematics, Politecnico Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
3.	Luiss Guido Carli, Viale Pola 12, 00198 Roma, Italy

Received February 2008 Revised February 2008 Published May 2008

Abstract
Related Papers

This paper deals with the development of a mathematical theory for complex socio-economical systems. The approach is based on the methods of the mathematical kinetic theory for active particles, which describes the evolution of large systems of interacting entities which are carriers of specific functions, in our case economical activities. The method is implemented with the concept of functional subsystems constituted by aggregated entities which have the ability of expressing socio-economical purposes and functions.

Keywords: stochastic systems., complexity, kinetic theory, social systems, economy.

Mathematics Subject Classification: Primary: 82D99, 91D10; Secondary: 91A1.

Citation: Giulia Ajmone Marsan, Nicola Bellomo, Massimo Egidi. Towards a mathematical theory of complex socio-economical systems by functional subsystems representation. Kinetic & Related Models, 2008, 1 (2) : 249-278. doi: 10.3934/krm.2008.1.249

[1]	P. Adda, J. L. Dimi, A. Iggidir, J. C. Kamgang, G. Sallet, J. J. Tewa. General models of host-parasite systems. Global analysis. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 1-17. doi: 10.3934/dcdsb.2007.8.1
[2]	Andrea L. Bertozzi. Preface to special issue on mathematics of social systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (5) : i-v. doi: 10.3934/dcdsb.2014.19.5i
[3]	Stefano Galatolo. Global and local complexity in weakly chaotic dynamical systems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1607-1624. doi: 10.3934/dcds.2003.9.1607
[4]	Krešimir Burazin, Marko Vrdoljak. Homogenisation theory for Friedrichs systems. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1017-1044. doi: 10.3934/cpaa.2014.13.1017
[5]	Denis de Carvalho Braga, Luis Fernando Mello, Carmen Rocşoreanu, Mihaela Sterpu. Lyapunov coefficients for non-symmetrically coupled identical dynamical systems. Application to coupled advertising models. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 785-803. doi: 10.3934/dcdsb.2009.11.785
[6]	Susanna Terracini, Juncheng Wei. DCDS-A Special Volume Qualitative properties of solutions of nonlinear elliptic equations and systems. Preface. Discrete & Continuous Dynamical Systems - A, 2014, 34 (6) : i-ii. doi: 10.3934/dcds.2014.34.6i
[7]	Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅱ: periodic boundary conditions. Communications on Pure & Applied Analysis, 2018, 17 (1) : 285-317. doi: 10.3934/cpaa.2018017
[8]	Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2357-2376. doi: 10.3934/cpaa.2017116
[9]	Brian Straughan. Shocks and acceleration waves in modern continuum mechanics and in social systems. Evolution Equations & Control Theory, 2014, 3 (3) : 541-555. doi: 10.3934/eect.2014.3.541
[10]	Leif Arkeryd. A kinetic equation for spin polarized Fermi systems. Kinetic & Related Models, 2014, 7 (1) : 1-8. doi: 10.3934/krm.2014.7.1
[11]	Salah-Eldin A. Mohammed, Tusheng Zhang. Large deviations for stochastic systems with memory. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 881-893. doi: 10.3934/dcdsb.2006.6.881
[12]	Bin Li, Hai Huyen Dam, Antonio Cantoni. A low-complexity zero-forcing Beamformer design for multiuser MIMO systems via a dual gradient method. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 297-304. doi: 10.3934/naco.2016012
[13]	Angelo B. Mingarelli. Nonlinear functionals in oscillation theory of matrix differential systems. Communications on Pure & Applied Analysis, 2004, 3 (1) : 75-84. doi: 10.3934/cpaa.2004.3.75
[14]	Sun-Sig Byun, Hongbin Chen, Mijoung Kim, Lihe Wang. L^p regularity theory for linear elliptic systems. Discrete & Continuous Dynamical Systems - A, 2007, 18 (1) : 121-134. doi: 10.3934/dcds.2007.18.121
[15]	Álvaro Pelayo, San Vű Ngọc. First steps in symplectic and spectral theory of integrable systems. Discrete & Continuous Dynamical Systems - A, 2012, 32 (10) : 3325-3377. doi: 10.3934/dcds.2012.32.3325
[16]	Santiago Capriotti. Dirac constraints in field theory and exterior differential systems. Journal of Geometric Mechanics, 2010, 2 (1) : 1-50. doi: 10.3934/jgm.2010.2.1
[17]	Roman Šimon Hilscher. On general Sturmian theory for abnormal linear Hamiltonian systems. Conference Publications, 2011, 2011 (Special) : 684-691. doi: 10.3934/proc.2011.2011.684
[18]	Ali K. Unver, Christian Ringhofer, M. Emir Koksal. Parameter extraction of complex production systems via a kinetic approach. Kinetic & Related Models, 2016, 9 (2) : 407-427. doi: 10.3934/krm.2016.9.407
[19]	N. Bellomo, A. Bellouquid. From a class of kinetic models to the macroscopic equations for multicellular systems in biology. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 59-80. doi: 10.3934/dcdsb.2004.4.59
[20]	Sabine Hittmeir, Sara Merino-Aceituno. Kinetic derivation of fractional Stokes and Stokes-Fourier systems. Kinetic & Related Models, 2016, 9 (1) : 105-129. doi: 10.3934/krm.2016.9.105

2016 Impact Factor: 1.261

American Institute of Mathematical Sciences