Network growth under the constraintof synchronization stabilityXingang WangOct.17,2010, Suzhou
Network growth under the constraint of synchronization stability Xingang Wang Oct. 17, 2010, Suzhou
Network is growingDriving forcesExternal demand: techonological and information networks, etcFunction requirement: social, economy and biology networks, etcBA growth model (SFN)[1]t=11. Growth2. Preferential attachement II, = k, / Z,k,t=2?& = n= 1Smoothgrowth[1] R.Albert and A.-L. Barabasi, Rev. Mod. Phys. 74, 47 (2002)
Network is growing External demand: techonological and information networks, etc. Driving forces Function requirement: social, economy and biology networks, etc. 1. Growth 2. Preferential attachement = j i i j k / k t =1 t = 2 t =n =1 Smooth growth ? BA growth model (SFN)[1] [1] R. Albert and A.-L. Barabasi, Rev. Mod. Phys. 74, 47 (2002)
Network growth in real worldTechnological networks (power-grid)[2]≥1Uneven growthn=4n=8n=9&≥1Intermitent growthEcological networks [3]t=3t=2t=0t=1Otherexamples:WwW,Internet,authorship,etc[2] P.Holme and B.J.Kim,Phys.Rev.E65, 066109(2002)[3] J.I.Perotti, et.al., Phys.Rev.Lett. 103. (2009)
Network growth in real world n = 9 n = 8 n = 4 Intermitent growth Uneven growth n 1 Ecological networks [3] t 1 t = 0 t =1 t = 2 t = 3 Other examples: WWW, Internet, authorship, etc. [2] P. Holme and B.J. Kim, Phys. Rev. E 65, 066109 (2002). [3] J.I. Perotti, et.al., Phys. Rev. Lett. 103. (2009). Technological networks (power-grid)[2]
dn(t) / dt ~ F(n,E,)E →Links ; →System Functional ityF →Nonlinear FunctionDynamicgrowth!
Dynamic growth ! dn(t)/ dt ~ F(n,,) → Links; →System Functional ity F →Nonlinear Function
Outline:1.Phenomenon2. Properties3.Mechanisms4. Consequences
Outline: 1. Phenomenon 2. Properties 3. Mechanisms 4. Consequences