We examine the evolution of the vocabulary of a group of individuals (linguistic agents) on a scale-free network, using Monte Carlo simulations and assumptions from evolutionary game theory. It is known that when the agents are arranged in a two-dimensional lattice structure and interact by...

We use the formulation of equilibrium statistical mechanics in order to study some important characteristics of language. Using a simple expression for the Hamiltonian of a language system, which is directly implied by the Zipf law, we are able to explain several characteristic features of human...

Competition between languages or cultural traits diffusing in the same geographical area is studied combining the model of Abrams and Strogatz with a model of human dispersal on an inhomogeneous substrate. Also, the effect of population growth is discussed. It is shown through numerical...

We have recently introduced a simple spatial computer simulation model to study the evolution of the linguistic diversity. The model considers processes of selective geographic colonization, linguistic anomalous diffusion and mutation. In the approach, we ascribe to each language a fitness...

Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization, linguistic anomalous diffusion and mutation, and interaction...

As a continuous opinion dynamics model, the information accumulation system (IAS) includes three basic mechanisms of the news, the inheritance and the diffusion as contributing to the information accumulation process of a system. A system is composed of agents who diffuse information through...

Time evolution of the relative density of speakers of an endangered language, Aromanian, which is spoken by a bilingual community in North-Western Greece, is approached theoretically by means of a two-state model and a three-state model. The same prestige and volatility parameters are used in...

We have recently investigated the evolution of linguistic diversity by means of a simple spatial model that considers selective geographic colonization, linguistic anomalous diffusion and mutation. In the model, regions of the lattice are characterized by the amount of resources available to...

In this work we study the dynamics of language competition. In Abrams and Strogatz [Modeling the dynamics of language death, Nature 424 (2003) 900], the extinction of one of the competing languages is predicted, although in some case the coexistence occurs. The preservation of both languages was...

We consider a model introduced recently [Nature 424(2003)900], for describing competition between two languages, which in typical situations predicts the extinction of one of them. We generalize it by introducing a spatial dependence in terms of a reaction–diffusion equation. We show that in...