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

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

Physica A: Statistical Mechanics and its Applications, 2015, vol. 430, issue C, 136-147

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.

Keywords: Language competitive model; State-dependent impulsive control; Order-k periodic solution; Multiple periodic solutions; Orbital stability (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:430:y:2015:i:c:p:136-147

DOI: 10.1016/j.physa.2015.02.064

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