On the modeling of nonlinear interactions in large complex systems

Applied Mathematics Letters

Volumn 23, Issue 11, 2010, Pages 1372-1377

  Bellomo, N ^a   Bianca, C ^a   Mongiovi M S ^b  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF PALERMO   (Italy)

Author keywords

Active particles; Functional subsystems; Kinetic theory; Living systems; Nonlinearity

Indexed keywords

ACTIVE PARTICLES; COMPLEX BIOLOGICAL SYSTEMS; COMPLEX SYSTEMS; FUNCTIONAL SUBSYSTEMS; LARGE SYSTEM; LIVING SYSTEMS; MATHEMATICAL APPROACH; NON-LINEARITY; NONLINEAR INTERACTIONS;

KINETIC THEORY;

EID: 77955924179     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2010.07.001     Document Type: Article

References (39)

1. N. Bellomo, C. Bianca, and M. Delitala Complexity analysis and mathematical tools towards the modelling of living systems Phys. Life Rev. 6 2009 144 175
2. N. Bellomo, and G. Forni Complex multicellular systems and immune competition: new paradigms looking for a mathematical theory Curr. Top. Dev. Biol. 81 2008 485 502
3. N. Bellomo, N.K. Li, and P.K. Maini On the foundations of cancer modelling: selected topics, speculations, and perspectives Math. Models Methods Appl. Sci. 18 2008 593 646
4. E.L. Cooper Evolution of immune system from self/not self to danger to artificial immune system Phys. Life Rev. 7 2010 55 78
5. S. De Lillo, M. Delitala, and C. Salvatori Modelling epidemics and virus mutations by methods of the mathematical kinetic theory for active particles Math. Models Methods Appl. Sci. 19 Suppl. 2009 1405 1426
6. C. Bianca, Mathematical modelling for keloid formation triggered by virus: malignant effects and immune system competition, Math. Models Methods Appl. Sci. 21 (2011) (in press).
7. G. Ajmone Marsan New paradigms towards the modelling of complex systems in behavioral economics Math. Comput. Modelling 50 2009 584 597
8. M.L. Bertotti, and M. Delitala On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders Math. Models Methods Appl. Sci. 18 2008 913 934
9. B. Carbonaro, and C. Giordano A second step towards mathematical models in psychology: a stochastic description of human feelings Math. Comput. Modelling 41 2005 587 614
10. F. Schweitzer Brownian Agents and Active Particles 2003 Springer Berlin
11. M. Talagrand Spin Glasses, a Challenge to Mathematicians 2003 Springer
12. M.B. Short, M.R. D'orsogna, V.B. Pasteur, G.E. Tita, P.J. Bratingham, A.L. Bertozzi, and L.B. Chayes A statistical model of criminal behavior Math. Models Methods Appl. Sci. 18 Suppl. 2008 1249 1268
13. M.B. Short, P.J. Bratingham, and A.L. Bertozzi Dissipation and hotspots in reactiondiffusion models of crime Proc. Natl. Acad. Sci. 2010 10.1073/pnas091921107
14. P.A. Jones, P.J. Brantigam, and L.R. Chayes Statistical models of criminal behavior: the effect of law enforcement actions Math. Models Methods Appl. Sci. 20 Suppl. 2010
15. N. Rodriguez, and A. Bertozzi Local existence and uniqueness of solutions to a PDE model for criminal behaviours Math. Models Methods Appl. Sci. 20 Suppl. 2010
16. I. Gallo, A. Barra, and L. Contucci Parameter evaluation of a simple mean-field model of social interaction Math. Models Methods Appl. Sci. 19 Suppl. 2009 1427 1440
17. M.B. Gordon, J.P. Nadal, D. Phan, and V. Semeshenko Discrete choices under social influence: generic properties Math. Models Methods Appl. Sci. 19 Suppl. 2009 1441 1483
18. Z. Zhao, A. Kirou, B. Ruszczycki, and N.F Johnson Dynamical clustering as a generator of complex system dynamics Math. Models Methods Appl. Sci. 19 Suppl. 2009 1539 1565
19. V. Coscia, and C. Canavesio First order macroscopic modelling of human crowds Math. Models Methods Appl. Sci. 18 Suppl. 2008 1217 1247
20. N. Bellomo, and C. Dogb On the modelling crowd dynamics from scaling to hyperbolic macroscopic models Math. Models Methods Appl. Sci. 18 Suppl. 2008 1317 1345
21. P. Degond, and S. Motsch Continuum limit of self-driven particles with orientation interaction Math. Models Methods Appl. Sci. 18 Suppl. 2008 1193 1216
22. 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 behaviour depends on topological rather than metric distance: evidence from a field study Proc. Natl. Acad. Sci. 105 2008 1232 1237
23. F. Cucker, and Jiu-Gang Dong On the critical exponent for flocks under hierarchical leadership Math. Models Methods Appl. Sci. 19 Suppl. 2009 1391 1404
24. N. Bellomo Modeling the hidinglearning dynamics in large living systems Appl. Math. Lett. 23 2010 907 911
25. L. Arlotti, and N. Bellomo Solution of a new class of nonlinear kinetic models of population dynamics Appl. Math. Lett. 9 1996 65 70
26. N. Bellomo, B. Firmani, and L. Guerri Bifurcation analysis for a nonlinear system of integro-differential equations modelling tumorimmune calls competition Appl. Math. Lett. 12 1999 39 44
27. A. Bellouquid, and M. Delitala Mathematical Modeling of Complex Biological Systems: A Kinetic Theory Approach 2006 Birkhuser Boston
28. C. Bianca On the modelling of space dynamics in the kinetic theory for active particles Math. Comput. Modelling 51 2010 72 83
29. A. Bellouquid, and C. Bianca Modelling aggregationfragmentation phenomena from kinetic to macroscopic scales Math. Comput. Modelling 52 2010 802 813
30. N. Bellomo, A. Bellouquid, J. Nieto, and J. Soler Complexity and mathematical tools toward the modelling of multicellular growing systems Math. Comput. Modelling 51 2010 441 451
31. N. Bellomo, A. Bellouquid, J. Nieto, and J. Soler Multiscale biological tissue models and flux-limited chemotaxis from binary mixtures of multicellular growing systems Math. Models Methods Appl. Sci. 20 2010 10.1142/ S0218202510004568
32. C. Cattani, and A. Ciancio Hybrid two scales mathematical tools for active particles modeling complex systems with learning hiding dynamics Math. Models Methods Appl. Sci. 17 2007 171 188
33. N. Bellomo, and M. Delitala On the coupling of higher and lower scales by the mathematical kinetic theory of active particles Appl. Math. Lett. 22 2008 646 650
34. C. Cattani, and A. Ciancio Qualitative analysis of second-order models of tumorimmune system competition Math. Comput. Modelling 47 2008 1339 1355
35. R. Brger, A. Garcia, and M. Kunik A generalized kinetic model of sedimentation of polydisperse suspensions with a continuous particle distribution Math. Models Methods Appl. Sci. 18 2008 1741 1786
36. S.K. Nemirovskii, and W. Fiszdon Chaotic quantized vortices and hydrodynamic processes in superfluid helium Rev. Modern Phys. 67 1995 37 84
37. S.K. Nemirovskii Gaussian model of vortex tangle in He II Phys. Rev. B 57 1998 5972 5986
38. S.K. Nemirovskii Kinetics of a network of vortex loops in He II and a theory of superfluid turbulence Phys. Rev. B 77 2008 214509
39. D. Jou, and M.S. Mongiov Non equilibrium temperature in well developed quantum turbulence Phys. Lett. A 373 2009 2306