Hybrid two scales mathematical tools for active particles modelling complex systems with learning hiding dynamics

被引：48
作者：
Cattani, C.
Ciancio, A.
机构：
[1] Univ Salerno, I-84084 Fisciano, Italy
[2] Univ Messina, Dept Math, I-98166 Messina, Italy
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2007年 / 17卷 / 02期
关键词：
stochastic dynamical systems; kinetic theory; population models; nonlinearity;
D O I：
10.1142/S0218202507001875
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with the derivation of hybrid mathematical structures to describe the behavior of large systems of active particles by ordinary differential equations with stochastic coefficients whose evolution is modelled by equations of the mathematical kinetic theory. A preliminary analysis shows how the above tools can be used to model complex systems of interest in applied sciences, with special attention to the immune competition.
引用
收藏
页码：171 / 187
页数：17
相关论文
共 34 条
[1]  
[Anonymous], 2003, J. Theor. Med
[2]   Generalized kinetic (Boltzmann) models: Mathematical structures and applications [J].
Arlotti, L ;
Bellomo, N ;
De Angelis, E .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (04) :567-591
[3]   Solution of a new class of nonlinear kinetic models of population dynamics [J].
Arlotti, L ;
Bellomo, N .
APPLIED MATHEMATICS LETTERS, 1996, 9 (02) :65-70
[4]   On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis [J].
Bellomo, N ;
Bellouquid, A .
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2006, 41 (02) :281-293
[5]  
Bellomo N, 2005, MATH MOD METH APPL S, V15, pIII
[6]   DYNAMICS OF TUMOR INTERACTION WITH THE HOST IMMUNE-SYSTEM [J].
BELLOMO, N ;
FORNI, G .
MATHEMATICAL AND COMPUTER MODELLING, 1994, 20 (01) :107-122
[7]   Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition [J].
Bellomo, N ;
Bellouquid, A ;
Delitala, M .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2004, 14 (11) :1683-1733
[8]   From the mathematical kinetic theory to modelling complex systems in applied sciences [J].
Bellomo, N .
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2004, 18 (4-5) :487-500
[9]  
BELLOMO N, 2006, DIFF EQUAT, V1, P1
[10]   Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems [J].
Bellomo, Nicola ;
Forni, Guido .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2006, 16 (07) :1001-1029
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