# American Institute of Mathematical Sciences

June  2008, 3(2): 221-238. doi: 10.3934/nhm.2008.3.221

## Network rewiring models

 1 Theoretical Physics, Blackett Laboratory, Imperial College London, South Kensington campus, London, SW7 2AZ, United Kingdom 2 Institute for Mathematical Sciences, Imperial College London, 53 Prince's Gate South Kensington, London, SW7 2PG, United Kingdom

Received  August 2007 Revised  March 2008 Published  March 2008

Recently we showed that a simple model of network rewiring could be solved exactly for any time and any parameter value. We also showed that this model can be recast in terms of several well known models of statistical physics such as Urn model and the Voter model. We also noted that it has been applied to a wide range of problems. Here we consider various generalisations of this model and include some new exact results.
Citation: T. S. Evans, A. D. K. Plato. Network rewiring models. Networks & Heterogeneous Media, 2008, 3 (2) : 221-238. doi: 10.3934/nhm.2008.3.221
 [1] Carlos M. Hernández-Suárez, Oliver Mendoza-Cano. Applications of occupancy urn models to epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 509-520. doi: 10.3934/mbe.2009.6.509 [2] Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks & Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255 [3] Simone Göttlich, Stephan Knapp. Semi-Markovian capacities in production network models. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3235-3258. doi: 10.3934/dcdsb.2017090 [4] Claus Kirchner, Michael Herty, Simone Göttlich, Axel Klar. Optimal control for continuous supply network models. Networks & Heterogeneous Media, 2006, 1 (4) : 675-688. doi: 10.3934/nhm.2006.1.675 [5] Tanka Nath Dhamala. A survey on models and algorithms for discrete evacuation planning network problems. Journal of Industrial & Management Optimization, 2015, 11 (1) : 265-289. doi: 10.3934/jimo.2015.11.265 [6] Gunhild A. Reigstad. Numerical network models and entropy principles for isothermal junction flow. Networks & Heterogeneous Media, 2014, 9 (1) : 65-95. doi: 10.3934/nhm.2014.9.65 [7] Dengfeng Sun, Issam S. Strub, Alexandre M. Bayen. Comparison of the performance of four Eulerian network flow models for strategic air traffic management. Networks & Heterogeneous Media, 2007, 2 (4) : 569-595. doi: 10.3934/nhm.2007.2.569 [8] Gianni Dal Maso, Flaviana Iurlano. Fracture models as $\Gamma$-limits of damage models. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1657-1686. doi: 10.3934/cpaa.2013.12.1657 [9] Fred Brauer. Some simple epidemic models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 1-15. doi: 10.3934/mbe.2006.3.1 [10] Abderrahman Iggidr, Josepha Mbang, Gauthier Sallet, Jean-Jules Tewa. Multi-compartment models. Conference Publications, 2007, 2007 (Special) : 506-519. doi: 10.3934/proc.2007.2007.506 [11] Michał Jóźwikowski, Mikołaj Rotkiewicz. Models for higher algebroids. Journal of Geometric Mechanics, 2015, 7 (3) : 317-359. doi: 10.3934/jgm.2015.7.317 [12] Zhiyu Wang, Yan Guo, Zhiwu Lin, Pingwen Zhang. Unstable galaxy models. Kinetic & Related Models, 2013, 6 (4) : 701-714. doi: 10.3934/krm.2013.6.701 [13] Carine Lucas, Antoine Rousseau. Cosine effect in ocean models. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 841-857. doi: 10.3934/dcdsb.2010.13.841 [14] Fred Brauer, Zhilan Feng, Carlos Castillo-Chávez. Discrete epidemic models. Mathematical Biosciences & Engineering, 2010, 7 (1) : 1-15. doi: 10.3934/mbe.2010.7.1 [15] Nur Aidya Hanum Aizam, Louis Caccetta. Computational models for timetabling problem. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 269-285. doi: 10.3934/naco.2014.4.269 [16] J. M. Cushing. Nonlinear semelparous Leslie models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 17-36. doi: 10.3934/mbe.2006.3.17 [17] Carlos Castillo-Chavez, Baojun Song. Dynamical Models of Tuberculosis and Their Applications. Mathematical Biosciences & Engineering, 2004, 1 (2) : 361-404. doi: 10.3934/mbe.2004.1.361 [18] Bruce D. Craven, Sardar M. N. Islam. Dynamic optimization models in finance: Some extensions to the framework, models, and computation. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1129-1146. doi: 10.3934/jimo.2014.10.1129 [19] Jacky Cresson, Bénédicte Puig, Stefanie Sonner. Stochastic models in biology and the invariance problem. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2145-2168. doi: 10.3934/dcdsb.2016041 [20] Shui-Nee Chow, Yongfeng Li. Model reference control for SIRS models. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 675-697. doi: 10.3934/dcds.2009.24.675

2018 Impact Factor: 0.871