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

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  • Nie, Lin-Fei
  • Teng, Zhi-Dong
  • Nieto, Juan J.
  • Jung, Il Hyo

Abstract

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.

Suggested Citation

  • Nie, Lin-Fei & Teng, Zhi-Dong & Nieto, Juan J. & Jung, Il Hyo, 2015. "State impulsive control strategies for a two-languages competitive model with bilingualism and interlinguistic similarity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 136-147.
    • Handle: RePEc:eee:phsmap:v:430:y:2015:i:c:p:136-147
    DOI: 10.1016/j.physa.2015.02.064
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    References listed on IDEAS

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    Cited by:

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