State impulsive control strategies for a two-languages competitive model with bilingualism and interlinguistic similarity

•A novel two languages competitive model with state pulse control strategies is introduced.•The model includes two control threshold values, it is different from the previous models.•Sufficient conditions on the existence and stability of stable periodic solutions are presented.•How the state-dependent pulse control strategies affect the endangered language is discussed.•Numerical simulations are carried out to illustrate the theoretical results.

For reasons of preserving endangered languages, we propose, in this paper, a novel two-languages competitive model with bilingualism and interlinguistic similarity, where state-dependent impulsive control strategies are introduced. The novel control model includes two control threshold values, which are different from the previous state-dependent impulsive differential equations. By using qualitative analysis method, we obtain that the control model exhibits two stable positive order-1 periodic solutions under some general conditions. Moreover, numerical simulations clearly illustrate the main theoretical results and feasibility of state-dependent impulsive control strategies. Meanwhile numerical simulations also show that state-dependent impulsive control strategy can be applied to other general two-languages competitive model and obtain the desired result. The results indicate that the fractions of two competitive languages can be kept within a reasonable level under almost any circumstances. Theoretical basis for finding a new control measure to protect the endangered language is offered.