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	Phase transitions in supercritical explosive percolation
	Chen, Wei ; Nagler, Jan ; Cheng, Xueqi ; Jin, Xiaolong ; Shen, Huawei ; Zheng, Zhiming ; D&apos ; Souza, Raissa M.
	2013
关键词	COMPLEX NETWORKS DISCONTINUOUS PERCOLATION RANDOM GRAPH COOPERATION COMPETITION EVOLUTION
英文摘要	Percolation describes the sudden emergence of large-scale connectivity as edges are added to a lattice or random network. In the Bohman-Frieze-Wormald model (BFW) of percolation, edges sampled from a random graph are considered individually and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function with asymptotic value of alpha, a constant. The BFW process has been studied as a model system for investigating the underlying mechanisms leading to discontinuous phase transitions in percolation. Here we focus on the regime alpha is an element of [0.6,0.95] where it is known that only one giant component, denoted C-1, initially appears at the discontinuous phase transition. We show that at some point in the supercritical regime C-1 stops growing and eventually a second giant component, denoted C-2, emerges in a continuous percolation transition. The delay between the emergence of C-1 and C-2 and their asymptotic sizes both depend on the value of a and we establish by several techniques that there exists a bifurcation point alpha(c) = 0.763 +/- 0.002. For a. [0.6, ac), C-1 stops growing the instant it emerges and the delay between the emergence of C-1 and C-2 decreases with increasing alpha. For alpha is an element of (alpha(c), 0.95], in contrast, C-1 continues growing into the supercritical regime and the delay between the emergence of C-1 and C-2 increases with increasing alpha. As we show, alpha(c) marks the minimal delay possible between the emergence of C-1 and C-2 (i.e., the smallest edge density for which C-2 can exist). We also establish many features of the continuous percolation of C-2 including scaling exponents and relations.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000319393900001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Physics, Fluids & Plasmas; Physics, Mathematical; SCI(E); 26; 5; 87
语种	英语
出处	SCI
出版者	physical review e
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/314344]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chen, Wei,Nagler, Jan,Cheng, Xueqi,et al. Phase transitions in supercritical explosive percolation. 2013-01-01.

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