Cellular Automata with Majority Rule on Evolving Network

The cellular automata discrete dynamical system is considered as the two-stage process: the majority rule for the change in the automata state and the rule for the change in topological relations between automata. The influence of changing topology to the cooperative phenomena, namely zero-temperature ferromagnetic phase transition, is observed.

[1]  Moshe Gitterman,et al.  Small-world phenomena in physics: the Ising model , 2000 .

[2]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[3]  Pontus Svenson,et al.  Damage spreading in small world Ising models. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  A. Fisher,et al.  The Theory of critical phenomena , 1992 .

[5]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[6]  Raúl Toral,et al.  Nonequilibrium transitions in complex networks: a model of social interaction. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  S. N. Dorogovtsev,et al.  Critical phenomena in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  D. Stauffer,et al.  SIMULATION OF CONSENSUS MODEL OF DEFFUANT et al. ON A BARABÁSI–ALBERT NETWORK , 2004 .

[9]  A. Heuer,et al.  過冷却Lennard‐Jones流体におけるホッピング:準ベイスン,待ち時間分布および拡散 , 2003 .

[10]  M. A. Novotny,et al.  Algorithmic scalability in globally constrained conservative parallel discrete event simulations of asynchronous systems , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Cristopher Moore,et al.  Disease spreading and percolation in small-world networks , 1999 .

[12]  James P. Crutchfield,et al.  Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations , 1993, Complex Syst..

[13]  Illés J. Farkas,et al.  Equilibrium Statistical Mechanicsof Network Structures , 2004 .

[14]  M. A. Novotny,et al.  On the Possibility of Quasi Small-World Nanomaterials , 2003 .

[15]  M. Newman Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Geoffrey Grinstein,et al.  Can complex structures be generically stable in a noisy world? , 2004, IBM J. Res. Dev..

[17]  J. Lebowitz,et al.  Statistical mechanics of probabilistic cellular automata , 1990 .

[18]  D. Stauffer,et al.  Ferromagnetic phase transition in Barabási–Albert networks , 2001, cond-mat/0112312.

[19]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[20]  A. Louisa,et al.  コロイド混合体における有効力 空乏引力から集積斥力へ | 文献情報 | J-GLOBAL 科学技術総合リンクセンター , 2002 .

[21]  M. Newman,et al.  Epidemics and percolation in small-world networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  Danuta Makowiec,et al.  Universality Class of Probabilistic Cellular Automata , 2002, ACRI.

[23]  M. Kuperman,et al.  Small world effect in an epidemiological model. , 2000, Physical review letters.

[24]  Hans J. Herrmann,et al.  Fast simulation of the Ising model using cellular automata , 1991 .

[25]  I. Farkas,et al.  Equilibrium statistical mechanics of network structures , 2004 .