期刊
JOURNAL OF NONLINEAR SCIENCE
卷 28, 期 1, 页码 235-268出版社
SPRINGER
DOI: 10.1007/s00332-017-9408-z
关键词
Dynamical networks; Cross-links; Microscopic model; Kinetic equation; Diffusion approximation; Mean-field limit; Aggregation-diffusion equation; Phase transitions; Fourier analysis; Bifurcations
资金
- Engineering and Physical Sciences Research Council (EPSRC) [EP/P031587/1, EP/M006883/1, EP/N014529/1, EP/P013651/1]
- Royal Society
- Wolfson Foundation through a Royal Society Wolfson Research Merit Award
- National Science Foundation (NSF) [RNMS11-07444]
- Wolfson Foundation through a Royal Society Wolfson Research Merit Award [WM130048]
- Vienna Science and Technology fund
- Vienna [LS13/029]
- Polish Ministry of Science and Higher Education Grant Iuventus Plus [0888/IP3/2016/74]
- Engineering and Physical Sciences Research Council [EP/P013651/1, EP/M006883/1, EP/P031587/1, EP/N014529/1] Funding Source: researchfish
- EPSRC [EP/P031587/1, EP/N014529/1, EP/M006883/1, EP/P013651/1] Funding Source: UKRI
We provide a numerical study of the macroscopic model of Barr, et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation-diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据