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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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    1. William J. Sutherland, 2003. "Parallel extinction risk and global distribution of languages and species," Nature, Nature, vol. 423(6937), pages 276-279, May.
    2. An, Zhecheng & Pan, Qiuhui & Yu, Guangying & Wang, Zhen, 2012. "The spatial distribution of clusters and the formation of mixed languages in bilingual competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4943-4952.
    3. Bakalis, Evangelos & Galani, Alexandra, 2012. "Modeling language evolution: Aromanian, an endangered language in Greece," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4963-4969.
    4. Tao Gong & Lan Shuai & Mónica Tamariz & Gerhard Jäger, 2012. "Studying Language Change Using Price Equation and Pólya-urn Dynamics," PLOS ONE, Public Library of Science, vol. 7(3), pages 1-12, March.
    5. Martin A. Nowak & Natalia L. Komarova & Partha Niyogi, 2002. "Computational and evolutionary aspects of language," Nature, Nature, vol. 417(6889), pages 611-617, June.
    6. Patriarca, Marco & Heinsalu, Els, 2009. "Influence of geography on language competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 174-186.
    7. Pinasco, J.P. & Romanelli, L., 2006. "Coexistence of Languages is possible," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 355-360.
    8. Stauffer, Dietrich & Castelló, Xavier & Eguíluz, Víctor M. & San Miguel, Maxi, 2007. "Microscopic Abrams–Strogatz model of language competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 835-842.
    9. Daniel M. Abrams & Steven H. Strogatz, 2003. "Modelling the dynamics of language death," Nature, Nature, vol. 424(6951), pages 900-900, August.
    10. Patriarca, Marco & Leppänen, Teemu, 2004. "Modeling language competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 296-299.
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