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On an optimal control strategy in a kinetic social dynamics model

Communications in Applied and Industrial Mathematics's Cover Image
Communications in Applied and Industrial Mathematics
Special Issue on Mathematical modelling for complex systems: multi-agents methods. Guest Editor: Elena De Angelis

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1. K. D. Bailey, Sociology and the new systems theory: Toward a theoretical synthesis. Suny Press, 1994.Search in Google Scholar

2. N. Bellomo, F. Colasuonno, D. Knopoff, and J. Soler, From a systems theory of sociology to modeling the onset and evolution of criminality, Networks & Heterogeneous Media, vol. 10, no. 3, 2015.10.3934/nhm.2015.10.421Search in Google Scholar

3. N. Bellomo, D. Knopoff, and J. Soler, On the diffcult interplay between life, “complexity", and mathematical sciences, Mathematical Models and Methods in Applied Sciences, vol. 23, no. 10, pp. 1861-1913, 2013.10.1142/S021820251350053XSearch in Google Scholar

4. M. Dolfin and M. Lachowicz, Modeling opinion dynamics: how the network enhances consensus, Networks & Heterogeneous Media, vol. 10, no. 4, pp. 421-441, 2015.10.3934/nhm.2015.10.877Search in Google Scholar

5. D. Knopoff, On a mathematical theory of complex systems on networks with application to opinion formation, Mathematical Models and Methods in Applied Sciences, vol. 24, no. 2, pp. 405-426, 2014.10.1142/S0218202513400137Search in Google Scholar

6. A. Bellouquid, E. De Angelis, and D. Knopoff, From the modeling of the immune hallmarks of cancer to a black swan in Biology, Mathematical Models and Methods in Applied Sciences, vol. 23, no. 5, pp. 949-978, 2013.10.1142/S0218202512500650Search in Google Scholar

7. D. A. Knopoff and J. M. Sánchez Sansó, A kinetic model for horizontal transfer and bacterial antibiotic resistance, International Journal of Biomathematics, vol. 10, no. 04, p. 1750051, 2017.10.1142/S1793524517500516Search in Google Scholar

8. M. Delitala, P. Pucci, and M. Salvatori, From methods of the mathematical kinetic theory for active particles to modeling virus mutations, Mathematical Models and Methods in Applied Sciences, vol. 21, no. supp01, pp. 843-870, 2011.10.1142/S0218202511005398Search in Google Scholar

9. M. Dolfin, L. Leonida, and N. Outada, Modeling human behavior in economics and social science, Physics of Life Reviews, 2017.10.1016/j.plrev.2017.06.02628711344Search in Google Scholar

10. M. L. Bertotti and M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Mathematical Models and Methods in Applied Sciences, vol. 14, no. 7, pp. 1061-1084, 2004.10.1142/S0218202504003544Search in Google Scholar

11. M. L. Bertotti and M. Delitala, Conservation laws and asymptotic behavior of a model of social dynamics, Nonlinear Analysis: Real World Applications, vol. 9, no. 1, pp. 183-196, 2008.10.1016/j.nonrwa.2006.09.012Search in Google Scholar

12. D. Knopoff, On the modeling of migration phenomena on small networks, Mathematical Models and Methods in Applied Sciences, vol. 23, no. 3, pp. 541-563, 2013.10.1142/S0218202512500558Search in Google Scholar

13. N. Bellomo, M. A. Herrero, and A. Tosin, On the dynamics of social conflicts: looking for the black swan, Kinetic and related models, vol. 6, no. 3, pp. 459-479, 2013.10.3934/krm.2013.6.459Search in Google Scholar

14. N. N. Taleb, The black swan: The impact of the highly improbable. Random house, 2007.Search in Google Scholar

15. M. Dolfin, D. Knopoff, L. Leonida, and D. M. A. Patti, Escaping the trap of "blocking": a kinetic model linking economic development and political competition, Kinetic and Related Models, vol. in press, 2016.10.3934/krm.2017016Search in Google Scholar

16. B. Düring, D. Matthes, and G. Toscani, Kinetic equations modelling wealth redistribution: a comparison of approaches, Physical Review E, vol. 78, no. 5, p. 056103, 2008.10.1103/PhysRevE.78.056103Search in Google Scholar

17. G. Ajmone Marsan, N. Bellomo, and L. Gibelli, Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics, Mathematical Models and Methods in Applied Sciences, vol. 26, no. 6, pp. 1051-1093, 2016.10.1142/S0218202516500251Search in Google Scholar

18. L. Pareschi and G. Toscani, Interacting multiagent systems: kinetic equations and Monte Carlo meth- ods. OUP Oxford, 2013.Search in Google Scholar

19. D. Cass and K. Shell, The Hamiltonian approach to dynamic economics. Academic Press, 2014.Search in Google Scholar

20. W. Stadler, Multicriteria Optimization in Engineering and in the Sciences, vol. 37. Springer Science & Business Media, 2013.Search in Google Scholar

21. G. Albi, M. Herty, and L. Pareschi, Kinetic description of optimal control problems and applications to opinion consensus, Communications in Mathematical Sciences, vol. 13, no. 6, pp. 1407-1429, 2015.10.4310/CMS.2015.v13.n6.a3Search in Google Scholar

22. A. Barrea and M. E. Hernández, Optimal control of a delayed breast cancer stem cells nonlinear model, Optimal Control Applications and Methods, vol. 37, no. 2, pp. 248-258, 2016.10.1002/oca.2164Search in Google Scholar

23. M. Gerdts, Optimal control of ODEs and DAEs. Walter de Gruyter, 2012.10.1515/9783110249996Search in Google Scholar

24. S. Lenhart and J. T. Workman, Optimal control applied to biological models. Crc Press, 2007.10.1201/9781420011418Search in Google Scholar

25. UNU-IHDP., Inclusive wealth report 2012: measuring progress toward sustainability. Cambridge University Press, 2012.Search in Google Scholar

26. M. Jarvis, G.-M. Lange, K. Hamilton, D. Desai, B. Fraumeni, B. Edens, S. Ferreira, H. Li, L. Chakraborti, W. Kingsmill, et al., The changing wealth of nations: measuring sustainable de- velopment in the new millennium. 2011.Search in Google Scholar

eISSN:
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Language:
English
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Journal Subjects:
Mathematics, Numerical and Computational Mathematics, Applied Mathematics