The model1.Growth (BA)2.Preferentialattachement(BA)3.Synchronizationstability(functionality）X, = F(X)+Zc,[H(X,)-H(X)]Synchronizablej=lCji =-a,jie / k,(aj} → adjacency matrixTheviewpointfromevolutionarynetworkNon-synchronizableNodeGrowthStructuredynamicsdynamics[4]A.E.Motter,et.al.,EPL69,334 (2005)
The model 1. Growth (BA) 2. Preferential attachement (BA) 3. Synchronization stability (functionality) Synchronizable Non-synchronizable = = + − n j i i j i H X j H Xi X F X c 1 ( ) [ ( ) ( )] cj i = −aj i / ki ,{aj i}→ adjacency matrix [4] A.E. Motter, et.al., EPL 69, 334 (2005). The viewpoint from evolutionary network Node dynamics Growth dynamics Structure
Time-scaleseparationt. → time unit for node additionT → charactering time for systemdynamics (synchronization)t.<<T:No contraint, BA SFNgt. >>T:Adiabaticgrowth,constraintactivatedgtg~T:EntangleddynamicsMSFoflogisticmapa=4Master stability function (MSF)[5]00.51.5R=, / Asynchronizabilitya102-2-≤-3.O = 2 ≤ ≤...≤a, :Eigen-spectrum of CAS-6.Necessary condition: R< R =, /o,0.00.51.01.52.0入[5] M. Barahona and L.M. Pecora,PRL89, 054101(2002)
Time-scale separation t g → time unit for node addition T → charactering time for system dynamics (synchronization) t T : g No contraint, BA SFN t T : g Adiabatic growth, constraint activated t T : g Entangled dynamics Master stability function (MSF)[5] [5] M. Barahona and L.M. Pecora, PRL 89, 054101 (2002). synchronizability 2 R = n / 0 . : = 1 2 n Eigen-spectrum of C Necessary condition: 2 1 R Rc = / 0.0 0.5 1.0 1.5 2.0 -7 -6 -5 -4 -3 -2 -1 0 1 0.5 1.5 MSF of logistic map a=4 1 2
A schematic plot on network growth2S(R.<R)2/2=Rn>n22(R<R)nn22mK(k[6]A.Arenas,et.al.,Phys.Rep.469,93(2008)
A schematic plot on network growth n 2 ~ n ~ ) ~ ( 2 Rc R c ) ~ (Rc R c n c c c n / 2 = R c n [6] A. Arenas, et.al., Phys. Rep. 469, 93 (2008).k k 2 1 ~ , 2 1 ~ 2 − 2 + n nc ?