Non-local network dynamics via fractional graph Laplacians

被引：17

作者：

Benzi, Michele ^{[1
]}

Bertaccini, Daniele ^{[2
,3
]}

Durastante, Fabio ^{[3
]}

Simunec, Igor ^{[1
]}

机构：

[1] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy

[2] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci 1, I-00133 Rome, Italy

[3] CNR, Ist Applicaz Calcolo M Picone, Via Pietro Castellino 111, I-80131 Rome, Italy

来源：

JOURNAL OF COMPLEX NETWORKS | 2020年 / 8卷 / 03期

关键词：

network dynamics; non-local dynamics; superdiffusion; matrix functions; power law decay; DECAY BOUNDS; MATRICES;

D O I：

10.1093/comnet/cnaa017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce non-local dynamics on directed networks through the construction of a fractional version of a non-symmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both directed and undirected graphs, showing the possibility of exploring the network employing random walks with jumps of arbitrary length. We also provide some examples of the applicability of the proposed dynamics, including consensus over multi-agent systems described by directed networks.

引用

页数：29

共 50 条

[31] ON FRACTIONAL HEAT EQUATIONS WITH NON-LOCAL INITIAL CONDITIONS
de Andrade, Bruno
Cuevas, Claudio
Soto, Herme
[J]. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2016, 59 (01) : 65 - 76
[32] Adaptively Enhancing Facial Expression Crucial Regions via a Local Non-local Joint Network
Shi, Guanghui
Mao, Shasha
Gou, Shuiping
Yan, Dandan
Jiao, Licheng
Xiong, Lin
[J]. MACHINE INTELLIGENCE RESEARCH, 2024, 21 (02) : 331 - 348
[33] A non-local fractional stress–strain gradient theory
Zaher Rahimi
Ghader Rezazadeh
Wojciech Sumelka
[J]. International Journal of Mechanics and Materials in Design, 2020, 16 : 265 - 278
[34] A NON-LOCAL PROBLEM FOR A DIFFERENTIAL EQUATION OF FRACTIONAL ORDER
Misenheimer, Nick
Kosmatov, Nickolai
[J]. DYNAMIC SYSTEMS AND APPLICATIONS, 2014, 23 (2-3): : 155 - 161
[35] On fractional non-local bodies with variable length scale
Sumelka, Wojciech
[J]. MECHANICS RESEARCH COMMUNICATIONS, 2017, 86 : 5 - 10
[36] Non-local fractional derivatives. Discrete and continuous
Abadias, Luciano
De Leon-Contreras, Marta
Torrea, Jose L.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 449 (01) : 734 - 755
[37] A comparative analysis of the RC circuit with local and non-local fractional derivatives
Rosales, J. J.
Filoteo, J. D.
Gonzalez, A.
[J]. REVISTA MEXICANA DE FISICA, 2018, 64 (06) : 647 - 654
[38] A fractional study of generalized Oldroyd-B fluid with ramped conditions via local & non-local kernels
Saeed, Syed Tauseef
Riaz, Muhammad Bilal
Baleanu, Dumitru
[J]. NONLINEAR ENGINEERING - MODELING AND APPLICATION, 2021, 10 (01): : 177 - 186
[39] Fractional calculus in solid mechanics: local versus non-local approach
Carpinteri, Alberto
Cornetti, Pietro
Sapora, Alberto
Di Paola, Mario
Zingales, Massimiliano
[J]. PHYSICA SCRIPTA, 2009, T136
[40] SIMULATING THE BEHAVIOR OF THE POPULATION DYNAMICS USING THE NON-LOCAL FRACTIONAL CHAFFEE-INFANTE EQUATION
Khater, Mostafa M. A.
Attia, Raghda A. M.
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2023, 31 (10)

← 1 2 3 4 5 →