Skip to main content

Forward Look at Research Perspectives

  • Chapter
  • First Online:
Complex Systems and Society

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

  • 1576 Accesses

Abstract

This chapter presents some on research perspectives. Various topics are treated focusing on the following issues: further analysis of the modeling of welfare policy in the case of interactions in a network and in open systems; generalization of the modeling approach to various systems of social sciences, for instance opinion formation; modeling the interplay of different types of dynamics also viewed as a tool for predicting rare events; and analytic problems posed by the application of models to the study of social phenomena.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Acemoglu, D., Robinson, J.A.: A theory of political transitions. American Economic Review 91(4), 938–963 (2001)

    Article  Google Scholar 

  2. Acemoglu, D., Robinson, J.A.: Economic Origins of Dictatorship and Democracy. Cambridge University Press (2006)

    Google Scholar 

  3. Agrawal, A., Cockburn, I., McHale, J.: Gone but not forgotten: knowledge flows, labor mobility, and enduring social relationships. Journal of Economic Geography 6(5), 571–591 (2006)

    Article  Google Scholar 

  4. Ajmone Marsan, G.: New paradigms towards the modelling of complex systems in Behavioral Economics. Mathematical and Computer Modelling 50(3–4), 584–597 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ajmone Marsan, G.: On the modelling and simulation of the competition for a secession under media influence by active particles methods and functional subsystems decomposition. Computer & Mathematics with Applications 57(5), 710–728 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Aletti, G., Naldi, G., Toscani, G.: First-order continuous models of opinion formation. SIAM Journal on Applied Mathematics 67(3), 837–853 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Arlotti, L., Bellomo, N.: Solution of a new class of nonlinear kinetic models of population dynamics. Applied Mathematics Letters 9(2), 65–70 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Arlotti, L., De Angelis, E.: On the initial value problem of a class of models of the kinetic theory for active particles. Applied Mathematics Letters 24(3), 257–263 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Arlotti, L., De Angelis, E., Fermo, L., Lachowicz, M., Bellomo, N.: On a class of integro-differential equations modeling complex systems with nonlinear interactions. Applied Mathematics Letters 25(3), 490–495 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Azoulay, P., Zivin, J.S.G., Sampat, B.N.: The diffusion of scientific knowledge across time and space: Evidence from professional transitions for the superstars of medicine. Working Paper 16683, National Bureau of Economic Research (2011)

    Google Scholar 

  11. Bagarello, F., Oliveri, F.: A phenomenological operator description of interactions between populations with applications to migration. Mathematical Models and Methods in Applied Sciences 23(3), 471–492 (2013)

    Article  MATH  Google Scholar 

  12. Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V., Orlandi, A., Parisi, G., Procaccini, A., Viale, M., Zdravkovic, V.: Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of the National Academy of Sciences 105(4), 1232–1237 (2008)

    Article  Google Scholar 

  13. Barabási, A.L.: The Science of Networks. Perseus, Cambridge MA (2022)

    Google Scholar 

  14. Barabási, A.L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Physica A 272(1), 173–187 (1999)

    Article  Google Scholar 

  15. Barbera, S., Maschler, M., Shalev, J.: Voting for voters: A model of electoral evolution. Games and Economic Behavior 37(1), 40–78 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Barrat, A., Bathélemy, M., Vespignani, A.: The Structure and Dynamics of Networks. Princeton University Press, Princeton NJ (2006)

    Google Scholar 

  17. Bastolla, U., Fortuna, M.A., Pascual-García, A., Ferrera, A., Luque, B., Bascompte, J.: The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature 458, 1018–1020 (2009)

    Article  Google Scholar 

  18. Bellomo, N., Bellouquid, A., Nieto, J., Soler, J.: On the asymptotic theory from microscopic to macroscopic growing tissue models: An overview with perspectives. Mathematical Models and Methods in Applied Sciences 22(1), 1130,001 (37 pages) (2012)

    Google Scholar 

  19. Bellomo, N., Herrero, M.A., Tosin, A.: On the dynamics of social conflicts looking for the Black Swan. Kinetic and Related Models 6(3), (2013)

    Google Scholar 

  20. Bellouquid, A., Delitala, M.: Mathematical modeling of complex biological systems: A kinetic theory approach. Modeling and Simulation In Science, Engineering and Technology. Birkhäuser, Boston (2006)

    Google Scholar 

  21. Berinsky, A.J., Burns, N., Traugott, M.W.: Who votes by mail?: A dynamic model of the individual-level consequences of voting-by-mail systems. Public Opinion Quarterly 65(2), 178–197 (2001)

    Article  Google Scholar 

  22. Bertotti, M.L.: Modelling taxation and redistribution: A discrete active particle kinetic approach. Applied Mathematics and Computation 217(2), 752–762 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Bertotti, M.L.: On a class of dynamical systems with emerging cluster structure. Journal of Differential Equations 249(11), 2757–2770 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  24. Bertotti, M.L., Delitala, M.: From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences. Mathematical Models and Methods in Applied Sciences 14(7), 1061–1084 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  25. Bertotti, M.L., Delitala, M.: Conservation laws and asymptotic behavior of a model of social dynamics. Nonlinear Analysis: Real World Applications 9(1), 183–196 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  26. Bertotti, M.L., Delitala, M.: On a discrete generalized kinetic approach for modelling persuader’s influence in opinion formation processes. Mathematical and Computer Modelling 48(7), 1107–1121 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  27. Bertotti, M.L., Delitala, M.: On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders. Mathematical Models and Methods in Applied Sciences 18(6), 913–934 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  28. Bertotti, M.L., Delitala, M.: Cluster formation in opinion dynamics: a qualitative analysis. Zeitschrift für angewandte Mathematik und Physik 61(4), 583–602 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  29. Bertotti, M.L., Modanese, G.: From microscopic taxation and redistribution models to macroscopic income distributions. Physica A 390(21–22), 3782–3793 (2011)

    Article  Google Scholar 

  30. Bisi, M., Spiga, G., Toscani, G.: Kinetic models of conservative economies with wealth redistribution. Communications in Mathematical Sciences 7(4), 901–916 (2009)

    MathSciNet  MATH  Google Scholar 

  31. Borjas, G.J.: Economic theory and international migration. International Migration Review 23(3), 457–485 (1989)

    Article  Google Scholar 

  32. Bressan, A.: Bifurcation analysis of a non-cooperative differential game with one weak player. Journal of Differential Equations 248(6), 1297–1314 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  33. Bressan, A.: Noncooperative differential games. A tutorial (2010). URL http://descartes.math.psu.edu/bressan/PSPDF/game-lnew.pdf. Lecture Notes for a Summer Course

  34. Bursik, R.J.: Social disorganization and theories of crime and delinquency: Problems and prospects. Criminology 26(4), 519–551 (1988)

    Article  Google Scholar 

  35. Camilli, F., Capuzzo Dolcetta, I., Falcone, M.: Preface. Networks and Heterogeneous Media 7(2), i–ii (2012). Special Issue on Mean Field Games

    Google Scholar 

  36. Cebula, R.J., Vedder, R.K.: A note on migration, economic opportunity, and the quality of life. Journal of Regional Science 13(2), 205–211 (1973)

    Article  Google Scholar 

  37. Comincioli, V., Della Croce, L., Toscani, G.: A Boltzmann-like equation for choice formation. Kinetic and Related Models 2(1), 135–149 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  38. Crescenzi, R., Rodriguez-Pose, A.: Innovation and Regional Growth in the European Union. Springer, Berlin, Heidelberg (2011)

    Book  Google Scholar 

  39. Cushing, B., Poot, J.: Crossing boundaries and borders: Regional science advances in migration modelling. Papers in Regional Science 83(1), 317–338 (2004)

    Google Scholar 

  40. De Lillo, S., Delitala, M., Salvatori, C.: Modelling epidemics and virus mutations by methods of the mathematical kinetic theory for active particles. Mathematical Models and Methods in Applied Sciences 19(1), 1405–1425 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  41. Dobson, D., St. Angelo, D.: Party identification and the floating vote: some dynamics. The American Political Science Review 69(2), 481–490 (1975)

    Google Scholar 

  42. Galam, S.: Collective beliefs versus individual inflexibility: The unavoidable biases of a public debate. Physica A 390(17), 3036–3054 (2011)

    Article  Google Scholar 

  43. Gauvin, L., Vannimenus, J., Nadal, J.P.: Phase diagram of a Schelling segregation model. The European Physical Journal B 70(2), 293–304 (2009)

    Article  Google Scholar 

  44. Gerber, A., Karlan, D.S., Bergan, D.: Does the media matter? A field experiment measuring the effect of newspapers on voting behavior and political opinions. Discussion paper 12, Yale University, Department of Economics (2006). Yale Working Papers on Economic Applications and Policy

    Google Scholar 

  45. Granovetter, M.S.: The strength of weak ties. American Journal of Sociology 78(6), 1360–1380 (1973)

    Article  Google Scholar 

  46. Guéant, O., Lasry, J., Lions, P.: Mean field games and applications. In: Paris-Princeton Lectures on Mathematical Finance 2010, Lecture Notes in Mathematics, vol. 2003, pp. 205–266. Springer, Berlin, Heidelberg (2011)

    Google Scholar 

  47. Helbing, D.: Quantitative sociodynamics: Stochastic methods and models of social interaction processes. Springer Verlag (2010)

    Google Scholar 

  48. Helbing, D., Sigmeier, J., Lämmer, S.: Self-organized network flows. Networks and Heterogeneous Media 2(2), 193–210 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  49. Jensen, M.B., Johnson, B., Lorenz, E., Lundvall, B.Å.: Forms of knowledge and modes of innovation. Research Policy 36(5), 680–693 (2007)

    Article  Google Scholar 

  50. Knopoff, D.: On the modeling of migration phenomena on small networks. Mathematical Models and Methods in Applied Sciences 23(3), 541–563 (2012)

    Article  Google Scholar 

  51. Langer, P., Nowak, M.A., Hauert, C.: Spatial invasion of cooperation. Journal of Theoretical Biology 250(4), 634–641 (2008)

    Article  MathSciNet  Google Scholar 

  52. Lasry, J.M., Lions, P.L.: Mean field games. Japanese Journal of Mathematics 2(1), 229–260 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  53. Maldarella, D., Pareschi, L.: Kinetic models for socio-economic dynamics of speculative markets. Physica A 391(3), 715–730 (2012)

    Article  Google Scholar 

  54. Markus, G.B., Converse, P.E.: A dynamic simultaneous equation model of electoral choice. The American Political Science Review 73(4), 1055–1070 (1979)

    Article  Google Scholar 

  55. Nowak, M.A.: Five rules for the evolution of cooperation. Science 314(5805), 1560–1563 (2006)

    Article  Google Scholar 

  56. Nowak, M.A., Ohtsuki, H.: Prevolutionary dynamics and the origin of evolution. Proceedings of the National Academy of Sciences 105(39), 14,924–14,927 (2008)

    Google Scholar 

  57. Nuño, J.C., Herrero, M.A., Primicerio, M.: A mathematical model of a criminal-prone society. Discrete and Continuous Dynamical Systems - Series S 4(1), 193–207 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  58. OECD: Regional Outlook, Building Resilient Regions for Stronger Economies. OECD Publishing (2011)

    Google Scholar 

  59. Ohtsuki, H., Pacheco, J.M., Nowak, M.A.: Evolutionary graph theory: Breaking the symmetry between interaction and replacement. Journal of Theoretical Biology 246(4), 681–694 (2007)

    Article  MathSciNet  Google Scholar 

  60. Olson, M.: Dictatorship, democracy, and development. American Political Science Review 87(3), 567–576 (1993)

    Article  Google Scholar 

  61. Piff, P.K., Stancato, D.M., Côté, S., Mendoza-Denton, R., Keltner, D.: Higher social class predicts increased unethical behavior. Proceedings of the National Academy of Sciences 109(11), 4086–4091 (2012)

    Google Scholar 

  62. Rand, D.G., Arbesman, S., Christakis, N.A.: Dynamic social networks promote cooperation in experiments with humans. Proceedings of the National Academy of Sciences 108(48), 19,193–19,198 (2011)

    Google Scholar 

  63. Sah, R.K.: Social osmosis and patterns of crime. Journal of Political Economy 99(6), 1272–1295 (1991)

    Article  Google Scholar 

  64. Scheffer, M., Bascompte, J., Brock, W.A., Brovkin, V., Carpenter, S.R., Dakos, V., Held, H., van Nes, E.H., Rietkerk, M., Sugihara, G.: Early-warning signals for critical transitions. Nature 461, 53–59 (2009)

    Article  Google Scholar 

  65. Short, M.B., D’Orsogna, M.R., Pasour, V.B., Tita, G.E., Brantingham, P.J., Bertozzi, A.L., Chayes, L.B.: A statistical model of criminal behavior. Mathematical Models and Methods in Applied Sciences 18(S1), 1249–1267 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  66. Taleb, N.N.: The Black Swan: The Impact of the Highly Improbable. Random House, New York City (2007)

    Google Scholar 

  67. Taleb, N.N.: Force et fragilité. Réflexions philosophiques et empiriques. Les Belles Lettres, Paris (2010)

    Google Scholar 

  68. Van Kempen, E.T.: The dual city and the poor: social polarisation, social segregation and life chances. Urban Studies 31(7), 995 (1994)

    Article  Google Scholar 

  69. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998)

    Article  Google Scholar 

  70. Wood, A.J., Ackland, G.J., Dyke, J.G., Williams, H.T.P., Lenton, T.M.: Daisyworld: A review. Reviews of Geophysics 46(1), RG1001 (23 pages) (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Nicola Bellomo, Giulia Ajmone, Andrea Tosin

About this chapter

Cite this chapter

Ajmone Marsan, G., Bellomo, N., Tosin, A. (2013). Forward Look at Research Perspectives. In: Complex Systems and Society. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7242-1_5

Download citation

Publish with us

Policies and ethics