Abstract
Language is characterized by both ecological properties and social properties, and competition is the basic form of language evolution. The rise and decline of one language is a result of competition between languages. Moreover, this rise and decline directly influences the diversity of human culture. Mathematics and computer modeling for language competition has been a popular topic in the fields of linguistics, mathematics, computer science, ecology, and other disciplines. Currently, there are several problems in the research on language competition modeling. First, comprehensive mathematical analysis is absent in most studies of language competition models. Next, most language competition models are based on the assumption that one language in the model is stronger than the other. These studies tend to ignore cases where there is a balance of power in the competition. The competition between two well-matched languages is more practical, because it can facilitate the co-development of two languages. A third issue with current studies is that many studies have an evolution result where the weaker language inevitably goes extinct. From the integrated point of view of ecology and sociology, this paper improves the Lotka–Volterra model and basic reaction–diffusion model to propose an “ecology–society” computational model for describing language competition. Furthermore, a strict and comprehensive mathematical analysis was made for the stability of the equilibria. Two languages in competition may be either well-matched or greatly different in strength, which was reflected in the experimental design. The results revealed that language coexistence, and even co-development, are likely to occur during language competition.
Highlights
Research on language evolution is crucial for understanding the diversity of human culture
This paper proposes an “ecology–society” computational model that describes the coexistence and co-development within language competition
C1 and c2 show the bidirectional attractive forces of two languages, while the original model in the previous section only represents unidirectional attractive force; and (2) Equations in the new model have positive and stable equilibriums under some conditions, which provides the possibility of co-existence or even co-development for two competitive languages
Summary
Research on language evolution is crucial for understanding the diversity of human culture. This paper proposes an “ecology–society” computational model that describes the coexistence and co-development within language competition. The common carrying capacity does not set the upper limit of the sum of the two components for one equilibrium This shows that the model is weaker than both the Lotka–Volterra model and the basic reaction–diffusion model for describing language coexistence. C1 and c2 show the bidirectional attractive forces of two languages, while the original model in the previous section only represents unidirectional attractive force; and (2) Equations in the new model have positive and stable equilibriums under some conditions, which provides the possibility of co-existence or even co-development for two competitive languages
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