Measures to sustain endangered languages: A bilingual competition model with sliding mode control

There are thousands of languages in the world, many of which are in danger of extinction due to language competition and evolution. Language is an aspect of culture, the rise, and fall of a language directly affects its corresponding culture. To preserve languages and prevent their mass extinction, it is crucial to develop a mathematical model of language coexistence. In this paper, we use a qualitative theory of ordinary differential equations to analyze the bilingual competition model, and obtain the trivial and non-trivial solutions of the bilingual competition model without sliding mode control, then analyze the stability of solutions and prove that solutions of the model have positive invariance. In addition, to maintain linguistic diversity and prevent mass extinction of languages, we propose a novel bilingual competition model with sliding control. The bilingual competition model is analyzed by proposing a sliding control policy to obtain a pseudo-equilibrium point. Meanwhile, numerical simulations clearly illustrate the effectiveness of the sliding mode control strategy. The results show that the likelihood of successful language coexistence can be increased by changing the status of languages and the value of monolingual-bilingual interaction, provides theoretical analysis for the development of policies to prevent language extinction.