Towards mathematical models in psychology: A stochastic description of human feelings

Mathematical Models and Methods in Applied Sciences

Volumn 12, Issue 10, 2002, Pages 1453-1490

  Carbonaro, Bruno ^a   Serra, Nicola ^a  

^a SECOND UNIVERSITY OF NAPLES   (Italy)

Author keywords

Dynamics of feelings; Stochastic dynamics; Stochastic integro differential equations

Indexed keywords

EID: 0036810991     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202502002197     Document Type: Article

References (28)

1. D. Ambrosi, N. Bellomo and L. Preziosi, Modelling tumor progression, heteregeneity and immune competition, J. Theor. Medicine 8 (2001).
2. U. an der Heiden, H. Schwegler and F. Tretter, Patterns of alcoholism - a mathematical model, Math. Models Methods Appl. Sci. 8 (1998) 521-541.
3. L. Arlotti and N. Bellomo, Population dynamics with stochastic interactions, Transp. Theory Statist. Phys. 24 (1995) 431-443.
4. L. Arlotti and N. Bellomo, Solution of a new class of models in applied sciences, Appl. Math. Lett. 9 (1996) 65-70.
5. L. Arlotti, N. Bellomo and K. Latrach, From the Jager and Segel model to kinetic population dynamics: Nonlinear evolution problems and application, Math. Comp. Modelling 30 (1999) 15-40.
6. L. Arlotti, N. Bellomo and M. Lachowicz, Kinetic equations modelling population dynamics, Transp. Theory Statist. Phys. 29 (2000) 125-139.
7. L. Arlotti, N. Bellomo and E. De Angelis, Generalized kinetic (Boltzmann) models - Mathematical structures and applications, Math. Models Methods Appl. Sci. 12 (2002).
8. N. Bellomo and L. Preziosi, Modelling, Mathematical Methods and Scientific Computation (CRC Press, 1995).
9. N. Bellomo, Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods, Math. Comp. Modelling 26 (1997) 13-34.
10. N. Bellomo and E. De Angelis, Strategies of applied mathematics towards an immuno mathematical theory on tumors and immune system interactions, Math. Models Methods Appl. Sci. 8 (1998) 1403-1429.
11. N. Bellomo and M. Lo Schiavo, Lecture Notes on the Generalized Boltzmann Equation (World Scientific, 2000).
12. N. Bellomo and M. Pulvirenti, Modelling in Applied Sciences - A Kinetic Theory Approach (Birkhäuser, 2000).
13. N. Bellomo, E. De Angelis, L. Graziano and A. Romano, Solution of nonlinear problems in applied sciences by generalized collocation methods and mathematica, Comp. Math. Appl. 41 (2001) 1343-1363.
14. B. Firmani, L. Guerri and L. Preziosi, Tumor/immune system competition with medically induced activation/disactivation, Math. Models Methods Appl. Sci. 9 (1999) 491-512.
15. U. Geigant, K. Ladizhansky and A. Mongilner, An integro-differential model for orientational distributions of F-actin cells, SIAM J. Appl. Math. 59 (1998) 787-809.
16. I. Guelfand and G. Chilov, Les Distributions (Dunod, 1965), Vols. 1-3.
17. A.K. Guts, V.V. Korobitsin, A.A. Laptev, L.A. Pautova and J.V. Frolova, Mathematical models of social systems Omsk State University (2000).
18. E. Jager and L. Segel, On the distribution of dominance in a population of interacting anonymous organisms, SIAM J. Appl. Math. 52 (1992), 1442-1468.
19. A.N. Kolmogorov and S.V. Fomin, Introductory Real Analysis (Dover, 1970).
20. M. Lachowicz and D. Wroszek, Nonlocal bilinear equations - Equilibrium solutions and diffusive limit, Math. Models Methods Appl. Sci. 11 (2001) 1391-1410.
21. P. Laurencot, The Lifshitz-Slyozov equation with encounters, Math. Models Methods Appl. Sci. 11 (2001) 731-748.
22. M. Lo Schiavo, Discrete kinetic cellular models of tumors immune system interactions, Math. Models Methods Appl. Sci. 6 (1996) 1187-1209.
23. J.E. Lund and K. Browers, Sinc Methods (SIAM, 1992).
24. W. Noll, Sine Methods (Springer, 1992).
25. S. Rinaldi, Laura and petrarch: An intriguing case of cyclical love dynamics, SIAM J. Appl. Math. 52 (1998) 1442-1468.
26. F. Stenger, Numerical Methods Based on Sinc and Analytic Functions (Springer, 1993).
27. C. Truesdell Introduction à la Mécanique Rationnelle des Milieux Continus (Dunod, 1993).
28. Z. Juming, L. Chengzou and S. Huiwen, Three-dimensional mathematical models of geological bodies and their graphical display, in Mathematical Geology and Geoinformatics, Proc. of the Thirtieth Int. Congress, 25 (1997).