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.