Naming Game on Multi-Community Network

We propose a new naming game model to imitate the process of human cognizing and naming a new object. Agents cognize an object through different name weights of its various words. The increase and decrease of names weight express that the name memory is enhanced and forgotten in human brain. Deleting names with low weights explains limited memory. On single-community playing our naming game, evolution can converge to global consensus asymptotically. The process of naming a new object is explained qualitatively by analyzing the number of total names, the number of different names and the average success rate. Optimal values of the deleting threshold and attenuation parameter induce the fastest convergence of the population, but very strong influences inhibit the convergence process. There exists a linear relationship between the two parameters to favor the rapid convergence. This paper also proposes a multi-community network model, which is composed of several communities, to simulate the evolution of different languages in various countries. Gaming on multi-community network model, the number of convergence names may be same as the number of communities. The stability of convergence names is related to the strength of communities and average degree, not related to the size of community. Stability analysis of differential equations is used to explain numerical computation. The agents in community hold a name and agents among communities hold several names, which are similar to multilingual and they can communicate with each other among communities.