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AXELROD'S MODEL FOR DISSEMINATION OF CULTURE |
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The java applet below visualizes the dynamics of Axelrod's model for dissemination of culture [1], including cultural dift [2], as well as the effect of different mass media [7,8,9]. In the context of Axelrod's model, we analyze the effect of cultural drift, as a random perturbation acting continuously on the system (noise) [2], whereas the mass media is modeled as an applied field that interacts with the agents [7]. The interaction dynamics of the elements among themselves and with the fields is based on the similarity between state vectors [1,2,7,8,9], defined as the fraction of components that these vectors have in common. Different types of fields, can be interpreted as various forms of mass media influences acting on social system [8,9]. We consider interaction fields that originate either externally an external forcing or from the contribution of a set of elements in the system an autonomous dynamics such as global or partial coupling functions. In the context of social phenomena, our scheme can be considered as a model for a social system interacting with global or local mass media that represent endogenous cultural influences or information feedback, as well as a model for a social system subject to an external cultural influence [7,8,9]. The
Model
The system consists of N elements as
the sites of a square lattice L x L. The state
Ci of element i is defined as
a vector of F
components σ = (σi1,σi2,...,σiF). In Axelrod's
model, the F
components of Ci correspond to
the cultural features describing the F-dimensional
culture of element i.
Each component σif can take any
of the q values in the set {0,1,..., q-1},
called cultural traits in Axelrod's model. As an initial condition,
each element is randomly and independently assigned one of the qF state vectors
with uniform probability.
For the case with mass media interaction, we introduce a vector field M with components (μi1,μi2,...,μiF). Formally, we treat the field at each element i as an additional neighbor of i with whom an interaction is possible. The field is represented as an additional element φ(i) such that σ φ(i) f = μif in the definition given below of the dynamics. The strength of the field is given by a constant parameter B that measures the probability of interaction with the field. When the values of B=0 and r=0, represent the original Axelrod's model interaction. The case where the elements on the lattice have a nonzero probability to interact with the field (B>0), we distinguish three types of fields. External
field:
i) Externally controlled mass media, propaganda : Spatially uniform and constant in time cultural field : External driving field acting uniformly on the system. It can be interpreted as a specific cultural state being imposed by controlled mass media on all elements of social system. Autonomous fields: ii) Global field (Global cultural trend) : Spatially uniform and time-dependent cultural field . At each time step the components of the field take the most abundant value exhibited by the F-th component of all the state vectors in the system. It gives a global coupling function of all the elements in the system. It can be interpreted as a global mass media influence which feeds back into the system the dominant global cultural trend. iii) Local field (Local cultural trend): Spatially non-uniform and time-dependent cultural field. At each time step the component of the field at node i takes the most frequent value in component F of the state vectors of the elements in the von Neumann neighborhood of element i. It can be interpreted as a local mass media (regional broadcast) which feeds back into the system the local dominant cultural trend. |
References:
[1] R.
Axelrod,
J. Conflict Res. 41, 203 (1997), Related
material by R. Axelrod
[2] K.
Klemm, V. M. Eguíluz, R. Toral, M. San Miguel, Global
culture:
A noise induced transition in finite systems, Phys. Rev. E 67,
045101(R) (2003).
[3] K.
Klemm,
V. M. Eguíluz, R.Toral, M. San Miguel, Nonequilibrium
transitions in complex networks:
a model of social interaction, Phys. Rev. E 67, 026120
(2003).
[4] Globalization,
Polarization, Cultural Drift and Social Networks. A presentation
in pdf.
[5] An
analysis of
the dissemination of culture in a one-dimensional world can be found in
K. Klemm, Victor M. Eguíluz, R. Toral, M. San Miguel, Globalization,
Polarization and Cultural Drift,
J. Economic Dynamics &
Control 29, 321 (2005). See also Role of
dimensionality in Axelrod's model
for the dissemination of culture, Physica A 327, 1
(2003).
[6]
Review paper on Voter and Axelord's models: M. San Miguel et al., Binary
and multivariate stochastic models of consensus formation,
Computing in Science and Engineering 7, Issue 6, 67 (2005).
[7] J.
C. González-Avella, M. G. Cosenza, K. Tucci, Nonequilibrium
transition induced by mass media in a model for social influence.
Phys. Rev. E 72, 065102(R) (2005).
[8] J.
C. González-Avella, V. M. Eguíluz, M. G.
Cosenza, K. Klemm, J. L.
Herrera and M. San Miguel,
Local versus global interactions in nonequilibrium transitions: A model
of social dynamics. Phys.
Rev. E 73, 046119 (2006).
[9] J.
C. González-Avella, M. G. Cosenza, K. Klemm, V. M.
Eguíluz and M. San
Miguel,
Information Feedback and Mass Media
Effects in Cultural Dynamics.
Journal of Artificial Societies and Social Simulation.
http://jasss.soc.surrey.ac.uk/10/3/9.html , 10, 1-17
(2006).
[10] Mass
Media Effects in Culrural Dynamics: The power of being subtle. A presentation in pdf.
[11] D. Centola, J. C.
González-Avella, V. M. Eguiluz and M.San Miguel, Homophily,
Cultural Drift and the Co-Evolution of Cultural Groups. Journal of Conflict Resolution,
arXiv:physics/0609213 (2007).
[12] F.
Vazquez, J. C. González-Avella, V. M. Eguiluz and M. San Miguel, Time scale
competition leading to fragmentation and recombination transitions in
the co-evolution of network and states. Physical Review E (2007).
[13] F. Vazquez, J. C. González-Avella, M. G. Cosenza, K.
Klemm, V. M.
Eguíluz and M. San
Miguel, Collective
Phenomena in Complex Social Networks. Submitted, Springer Verlag
(2007). |
The system evolves by iterating the following steps: (1) Select at random an element i on the lattice. (2) Select the source of interaction j. With probability B set j=φ(i) as an interaction with the field. Otherwise, choose element j at random among the four nearest neighbors (the von Neumann neighborhood) of i on the lattice. (3)
Calculate the overlap
(number
of shared components). If 0 < overlap < F,
the sites i
and j
interact with probability overlap/F.
In case of interaction,
choose h
randomly such that σih ≠ σjh and set σih = σjh. When we consider the effect of cultural drift , in the algorithm we include a fifth step in the iterated loop of the model. (5) With probability r, randomly choosing i ∈ { 1, . . . ,N} , f ∈ { 1, . . . ,F} and s ∈{0, . . . ,q-1} and setting σif = s;. |
| A
guide for using the applet |
| Here it is
assumed that
you are familiar with the dynamical rules of the model. If not,
reference
[5,6,7,8] above should be helpful.
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