A mean-field approach to self-interacting networks, convergence and regularity

被引：5

作者：

Catellier, Remi ^{[1
]}

D'Angelo, Yves ^{[1
]}

Ricci, Cristiano ^{[2
]}

机构：

[1] Univ Cote dAzur, LJAD, CNRS, INRIA, Nice, France

[2] Scuola Normale Super Pisa, Pisa, Italy

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2021年 / 31卷 / 13期

关键词：

Interacting particle system; mathematical biology; hypoelliptic PDEs; APPROXIMATION; DYNAMICS; SYSTEMS; GROWTH; MODEL;

D O I：

10.1142/S0218202521500573

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a network of mycelium is analyzed as representative case, and the generality of the modeling choices are discussed. Convergence of the empirical density for the particle system to its mean-field limit is proved, and a result of regularity for the solution is presented.

引用

收藏

页码：2597 / 2641

页数：45

相关论文

共 30 条

[1] Statistical mechanics of complex networks [J].

Albert, R ;

Barabási, AL .

REVIEWS OF MODERN PHYSICS, 2002, 74 (01) :47-97

[2]

Barrat A., 2008, Dynamical Processes on Complex Networks

[3] Self-interacting diffusions [J].

Benaïm, M ;

Ledoux, M ;

Raimond, O .

PROBABILITY THEORY AND RELATED FIELDS, 2002, 122 (01) :1-41

[4] Self-interacting diffusions IV: Rate of convergence [J].

Benaim, Michel ;

Raimond, Olivier .

ELECTRONIC JOURNAL OF PROBABILITY, 2011, 16 :1815-1843

[5] Growth and function of fungal mycelia in heterogeneous environments [J].

Boswell, GP ;

Jacobs, H ;

Davidson, FA ;

Gadd, GM ;

Ritz, K .

BULLETIN OF MATHEMATICAL BIOLOGY, 2003, 65 (03) :447-477

[6]

Boswell Graeme P., 2012, Fungal Biology Reviews, V26, P30, DOI 10.1016/j.fbr.2012.02.002

[7] Linking hyphal growth to colony dynamics: Spatially explicit models of mycelia [J].

Boswell, Graeme P. ;

Hopkins, Steven .

FUNGAL ECOLOGY, 2008, 1 :143-154

[8] On the mean field approximation of a stochastic model of tumour-induced angiogenesis [J].

Capasso, V ;

Flandoli, F. .

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2019, 30 (04) :619-658

[9] Unifying evolutionary dynamics:: From individual stochastic processes to macroscopic models [J].

Champagnat, N ;

Ferrière, R ;

Méléard, S .

THEORETICAL POPULATION BIOLOGY, 2006, 69 (03) :297-321

[10] Invasion and adaptive evolution for individual-based spatially structured populations [J].

Champagnat, Nicolas ;

Meleard, Sylvie .

JOURNAL OF MATHEMATICAL BIOLOGY, 2007, 55 (02) :147-188