第2期 王龙,等:复杂网络上的群体决策 ·107· [52]STRO GA TZ S H.Sync:the emerging science of spon- servation laws for the voter model in complex networks taneous order [M].New York:Hyperion Press,2003. [U].Europhys Lett,2005,69:228-234, [53]KURAMOTO Y.Chemical oscillations,waves,and [71]LI PP,ZHENGD F,HUI P M.Dynamics of opinion turbulence [M].Berlin:Springer-Verlag,1984 formation in a smalFworld network [J ]Phys Rev E, [54]BARTOLOZZI M,LEINWEBER D B,THOMAS A 2006,73:056128. W.Stochastic opinion formation in scale-free networks [72]LAMBIOTTE R.How does degree heterogeneity af- [U].Phys Rev E,2005,72:046113. fect an order-disorder transition [J ]Europhys Lett, [55]JUNG W S,MOON H T,STANLEY H E.Dynamics 2007,78:68002. of clustered opinions in complex networks EB/OL ] [73]LAMBIOTTE R,AUSLOOS M.Coexistence of oppo- [2007-08-03].http //arxiv.org/abs/physics/0702108 site opinions in a network with communities [J].J Stat [56]GLAUBER R.Time-dependent statistics of the Ising Mech,2007,8:08026. model [J].Math Phys,1963,4:294-307. [74 SOUSA A O.Bounded confidence model on a still [57]SZNAJD-WERON K.Dynamical model of Ising spins growing scale-free network EB/OL ][2005-01-19]. [U].Phys Rev E,2004,70:037104. http //arxiv.org/abs/cond-mat/0406766v2. [58]GALAM S.Rational group decision making:a random [75]DEFFUANT G,NEAU D,AMBLARD F,et al.Mix- field Ising model at T=0 [J ]Physica A,1997,238: ing beliefs among interacting agents[J].Adv Complex 6680. Syst,2000(3):8798. [59]KWAK W,YANGJ S,SOHN J I,et al.Critical be- [76]FORTUNATO S.Damage spreading and opinion dy- havior of the majority voter model is independent of namics on scale-free networks [J].Physica A,2005, transition rates [J].Phys Rev E,2007,75:061110. 348:683-690. [60]SOOD V,REDNER S.Voter model on heterogeneous [77]LORENZ J.Continuous opinion dynamics of multidi- graphs [J].Phys Rev Lett,2005,94:178701. mensional allocation problems under bounded confi- [61]MOBILIA M,PETERSEN A,REDNER S.On the dence:More dimensions lead to better chances for con- role of zealotry in the voter model [J].J Stat Mech, sensus EB/OL ][2007-08-21 ]http://acseg.univ- 2007,8:08029. mrs.fr/document/Lorenzpapier.pdf. [62]CHEN P,REDN ER S.Majority rule dynamics in finite [78]GALAM S.Social paradoxes of majority rule voting dimensions [J ]Phys Rev E,2005,71:036101 and renormalization group [J].J Stat Phys,1990,61: (63]LAMBIOTTE R,AUSLOOS M,HOL YSTJ A.Ma- 943-951. jority model on a network with communities [J].Phys [79]GALAM S.Heterogeneous beliefs,segregation,and RevE,2007,75:030101. extremism in the making of public opinions [J].Phys [64]KRAPIVSKY PL,REDNER S.Dynamics of majority RevE,2005,71:046123. rule in two-state interacting spin systems [J ]Phys [80]GALAM S.Contrarian deterministic effects on opinion Rev Lett,2003,90(23):238701. dynamics:the hung elections scenario [J].Physica A, [65]GABBA Y M.The effects of nonlinear interactions and 2004,333:453460. network structure in small group opinion dynamics [J]. [81]GALAM S,BORGHESI C.Chaotic,staggered,and Physica A,2007,373:118126. polarized dynamics in opinion forming:the contrarian [66]LIGGETT T M.Stochastic interaction systems:con effect [J].Phys Rev E,2006,73:066118. tact,voter,and exclusion processes [M].New York: [82]GUZMAN-VARGAS L,HERNANDEZ-PEREZ R. Springer-Verlag,1999. Small-world topology and memory effects on decision [67]KRAPIVSKY PL.Kinetics of monomermonomer sur- time in opinion dynamics [J ]Physica A,2006,372: face catalytic reactions [J ]Phys Rev A,1992,45: 326332. 10671072. [83]GEKL E S,PELITIL,GALAM S.Opinion dynamics [68]SUCHECKI K,HOL YSTJ A.Voter model on Sier- in a three-choice system [J ]Euro PhysJ B,2005,45: pinski fractals [J].Physica A,2006,362:338-344. 569575. [69]CASTELLANO C,VILONE D,VESPIGNANI A. [84]STAUFFER D,SA HIMI M.Can a few fanatics influ Incomplete ordering of the voter model on smalFworld ence the opinion of a large segment of a society [J ] networks [J ]Europhys Lett,2003,63:153-158. Euro Phys J B,2007,57:147152. [70]SUCHECKI K,EGUILUZ V M,MIGUEL M S.Com [85]PETTER H,NEWMAN M EJ.Nonequilibrium phase 1994-2009 China Academic Journal Electronic Publishing House.All rights reserved.http://www.cnki.net[ 52 ] STRO GA TZ S H. Sync : the emerging science of spon2 taneous order [ M]. New York : Hyperion Press , 2003. [53 ] KURAMO TO Y. Chemical oscillations , waves , and turbulence [ M]. Berlin : Springer2Verlag , 1984. [54 ] BARTOLOZZI M , L EINWEBER D B , THOMAS A W. Stochastic opinion formation in scale2free networks [J ]. Phys Rev E , 2005 , 72 : 046113. [55 ] J UN G W S , MOON H T , STANL EY H E. Dynamics of clustered opinions in complex networks [ EB/ OL ]. [2007208203 ]. http :/ / arxiv. org/ abs/ physics/ 0702108. [56 ] GLAUBER R. Time2dependent statistics of the Ising model [J ]. Math Phys , 1963 , 4 : 2942307. [57 ] SZNAJD2WERON K. Dynamical model of Ising spins [J ]. Phys Rev E , 2004 , 70 : 037104. [58 ] GALAM S. Rational group decision making : a random field Ising model at T = 0 [J ]. Physica A , 1997 , 238 : 66280. [59 ] KWA K W , YAN G J S , SO HN J I , et al. Critical be2 havior of the majority voter model is independent of transition rates [J ]. Phys Rev E , 2007 , 75 : 061110. [60 ] SOOD V , REDN ER S. Voter model on heterogeneous graphs [J ]. Phys Rev Lett , 2005 , 94 : 178701. [61 ] MOBIL IA M , PETERSEN A , REDN ER S. On the role of zealotry in the voter model [J ]. J Stat Mech , 2007 , 8 : 08029. [62 ] CHEN P , REDNER S. Majority rule dynamics in finite dimensions [J ]. Phys Rev E , 2005 , 71 : 036101. [63 ] LAMBIO TTE R , AUSLOOS M , HOL YST J A. Ma2 jority model on a network with communities [J ]. Phys Rev E , 2007 , 75 : 030101. [64 ] KRAPIVSKY P L , REDN ER S. Dynamics of majority rule in two2state interacting spin systems [J ]. Phys Rev Lett , 2003 , 90 (23) : 238701. [65 ] GABBA Y M. The effects of nonlinear interactions and network structure in small group opinion dynamics [J ]. Physica A , 2007 , 373 : 1182126. [66 ] L IGGETT T M. Stochastic interaction systems: con2 tact , voter , and exclusion processes [ M ]. New York : Springer2Verlag , 1999. [ 67 ] KRAPIVSKY P L. Kinetics of monomer2monomer sur2 face catalytic reactions [J ]. Phys Rev A , 1992 , 45 : 106721072. [68 ] SUCHECKI K , HOL YST J A. Voter model on Sier2 pinski fractals [J ]. Physica A , 2006 , 362 : 3382344. [ 69 ] CASTELLANO C , VILON E D , V ESPIGNANI A. Incomplete ordering of the voter model on small2world networks [J ]. Europhys Lett , 2003 , 63 : 1532158. [ 70 ] SUCHECKI K , EGUILUZ V M , MIGU EL M S. Con2 servation laws for the voter model in complex networks [J ]. Europhys Lett , 2005 , 69 : 2282234. [ 71 ] L I P P , ZHEN G D F , HU I P M. Dynamics of opinion formation in a small2world network [J ]. Phys Rev E , 2006 , 73 : 056128. [72 ] LAMBIO TTE R. How does degree heterogeneity af2 fect an order2disorder transition [J ]. Europhys Lett , 2007 , 78 : 68002. [ 73 ] LAMBIO TTE R , AUSLOOS M. Coexistence of oppo2 site opinions in a network with communities [J ]. J Stat Mech , 2007 , 8 : 08026. [ 74 ] SOUSA A O. Bounded confidence model on a still growing scale2free network [ EB/ OL ]. [ 2005201219 ]. http :/ / arxiv. org/ abs/ cond2mat/ 0406766v2. [ 75 ] DEFFUAN T G, NEAU D , AMBLARD F , et al. Mix2 ing beliefs among interacting agents[J ]. Adv Complex Syst , 2000 (3) : 87298. [76 ] FORTUNA TO S. Damage spreading and opinion dy2 namics on scale2free networks [J ]. Physica A , 2005 , 348 : 6832690. [77 ] LORENZ J. Continuous opinion dynamics of multidi2 mensional allocation problems under bounded confi2 dence : More dimensions lead to better chances for con2 sensus [ EB/ OL ]. [ 2007208221 ]. http :/ / acseg. univ2 mrs.fr/ document/ Lorenzpapier. pdf. [78 ] GALAM S. Social paradoxes of majority rule voting and renormalization group [J ]. J Stat Phys , 1990 , 61 : 9432951. [79 ] GALAM S. Heterogeneous beliefs , segregation , and extremism in the making of public opinions [J ]. Phys Rev E , 2005 , 71 : 046123. [80 ] GALAM S. Contrarian deterministic effects on opinion dynamics: the hung elections scenario [J ]. Physica A , 2004 , 333 : 4532460. [81 ] GALAM S , BORGHESI C. Chaotic , staggered , and polarized dynamics in opinion forming : the contrarian effect [J ]. Phys Rev E , 2006 , 73 : 066118. [ 82 ] GUZMAN2VARGAS L , HERNANDEZ2PEREZ R. Small2world topology and memory effects on decision time in opinion dynamics [J ]. Physica A , 2006 , 372 : 3262332. [83 ] GEKL E S , PEL ITI L , GALAM S. Opinion dynamics in a three2choice system [J ]. Euro Phys J B , 2005 , 45 : 5692575. [84 ] STAU FFER D , SA HIMI M. Can a few fanatics influ2 ence the opinion of a large segment of a society [J ]. Euro Phys J B , 2007 , 57 : 1472152. [ 85 ] PETTER H , N EWMAN M E J. Nonequilibrium phase 第 2 期 王 龙 ,等 :复杂网络上的群体决策 ·107 ·