On mean field solutions of kinetic exchange opinion models

We present here the exact solution of an infinite range, discrete, opinion formation model. The model shows an active-absorbing phase transition, similar to that numerically found in its recently proposed continuous version [Lallouache et al., Phys. Rev E 82, 056112 (2010)]. Apart from the two-agent interactions here we also report the effect of having three-agent interactions. The phase diagram has a continuous transition line (two-agent interaction dominated) and a discontinuous transition line (three-agent interaction dominated) separated by a tricritical point.

[1]  Robert A. Meyers,et al.  Encyclopedia of Complexity and Systems Science , 2009 .

[2]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.

[3]  Bikas K. Chakrabarti,et al.  Pareto Law in a Kinetic Model of Market with Random Saving Propensity , 2004 .

[4]  H. Hinrichsen Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[5]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[6]  Anirban Chakraborti,et al.  Opinion formation in kinetic exchange models: spontaneous symmetry-breaking transition. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Soumyajyoti Biswas,et al.  Phase transitions and non-equilibrium relaxation in kinetic models of opinion formation , 2010, ArXiv.

[8]  Santo Fortunato The Sznajd Consensus Model with Continuous Opinions , 2005 .

[9]  V Schwämmle,et al.  Different topologies for a herding model of opinion. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[11]  S. Lübeck,et al.  UNIVERSAL SCALING BEHAVIOR OF NON-EQUILIBRIUM PHASE TRANSITIONS , 2004 .

[12]  Bikas K. Chakrabarti,et al.  Statistical mechanics of money: how saving propensity affects its distribution , 2000, cond-mat/0004256.

[13]  B. Latané,et al.  Statistical mechanics of social impact. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[14]  Dietrich Stauffer Sociophysics simulations , 2003, Comput. Sci. Eng..

[15]  José S Andrade,et al.  Tricritical point in explosive percolation. , 2010, Physical review letters.

[16]  W. Kinzel Phase transitions of cellular automata , 1985 .

[17]  Eytan Domany,et al.  Equivalence of Cellular Automata to Ising Models and Directed Percolation , 1984 .

[18]  K. Kacperski,et al.  Phase transitions and hysteresis in a cellular automata-based model of opinion formation , 1996 .

[19]  G. Toscani,et al.  Kinetic models of opinion formation , 2006 .

[20]  Parongama Sen,et al.  Model of binary opinion dynamics: Coarsening and effect of disorder. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Parongama Sen Phase transitions in a two-parameter model of opinion dynamics with random kinetic exchanges. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Arnab Chatterjee,et al.  Kinetic models for wealth exchange on directed networks , 2009, 0901.2857.

[23]  Anindya S. Chakrabarti,et al.  An almost linear stochastic map related to the particle system models of social sciences , 2011, 1101.3617.

[24]  Frank Schweitzer,et al.  Phase transitions in social impact models of opinion formation , 2000 .

[25]  B. Latané,et al.  From private attitude to public opinion: A dynamic theory of social impact. , 1990 .

[26]  T. Schelling Models of Segregation , 1969 .

[27]  F Bagnoli,et al.  Nature of phase transitions in a probabilistic cellular automaton with two absorbing states. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[29]  S. Galam,et al.  Sociophysics: A new approach of sociological collective behaviour. I. mean‐behaviour description of a strike , 1982, 2211.07041.

[30]  Bikas K. Chakrabarti,et al.  Kinetic exchange models for income and wealth distributions , 2007, 0709.1543.

[31]  Guillaume Deffuant,et al.  Mixing beliefs among interacting agents , 2000, Adv. Complex Syst..

[32]  Serge Galam,et al.  SOCIOPHYSICS: A REVIEW OF GALAM MODELS , 2008, 0803.1800.