 Patterns of a spatial exploration under time evolution of the attractiveness: Persistent nodes, degree distribution, and spectral propertiesRoberto da Silva Physica A: Statistical Mechanics and its Applications, 2018, vol. 500, issue C, 60-71 Abstract: This work explores the features of a graph generated by agents that hop from one node to another node, where the nodes have evolutionary attractiveness. The jumps are governed by Boltzmann-like transition probabilities that depend both on the euclidean distance between the nodes and on the ratio (β) of the attractiveness between them. It is shown that persistent nodes, i.e., nodes that never been reached by this special random walk are possible in the stationary limit differently from the case where the attractiveness is fixed and equal to one for all nodes (β=1). Simultaneously, one also investigates the spectral properties and statistics related to the attractiveness and degree distribution of the evolutionary network. Finally, a study of the crossover between persistent phase and no persistent phase was performed and it was also observed the existence of a special type of transition probability which leads to a power law behaviour for the time evolution of the persistence. Keywords: Spatial exploration; Persistence; Networks; Random matrices (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:500:y:2018:i:c:p:60-71 DOI: 10.1016/j.physa.2018.02.015 Access Statistics for this article Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis More articles in Physica A: Statistical Mechanics and its Applications from Elsevier |
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