Advanced search
Publication Cover
The Journal of Mathematical Sociology Volume 16, 1990 - Issue 1
Submit an article Journal homepage
41
Views
40
CrossRef citations to date
0
Altmetric
Original Articles

A mathematical model for the dynamics of interactions between a unilingual and a bilingual population: Persistence versus extinction

I. Baggs Department of Mathematics, University of Alberta, Edmonton, T6G 2G1, Canada
&
H. I. Freedman Applied Mathematics Institute, University of Alberta, Edmonton, T6G 2G1, Canada
Pages 51-75 | Published online: 26 Aug 2010

Citations (40)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (8)

John Wyburn. (2020) The need for language planning to address English-language media pressures on minority language survival in bilingual populations. Journal of the Operational Research Society 71:9, pages 1357-1374.
Read now
John Wyburn. (2018) Media pressures on Welsh language preservation. The Journal of Mathematical Sociology 42:1, pages 37-46.
Read now
J. F. Gomez-Aguilar. (2017) New bilingualism model based on fractional operators with Mittag-Leffler kernel. The Journal of Mathematical Sociology 41:3, pages 172-184.
Read now
Lorelei Koss. (2015) Differential equations in literature, poetry and film. Journal of Mathematics and the Arts 9:1-2, pages 1-16.
Read now
JOHN WYBURN & JOHN HAYWARD. (2010) A Model of Language-Group Interaction and Evolution Including Language Acquisition Planning. The Journal of Mathematical Sociology 34:3, pages 167-200.
Read now
J Wyburn & J Hayward. (2009) OR and language planning: modelling the interaction between unilingual and bilingual populations. Journal of the Operational Research Society 60:5, pages 626-636.
Read now
JOHN WYBURN & JOHN HAYWARD. (2008) The Future of Bilingualism: An Application of the Baggs and Freedman Model. The Journal of Mathematical Sociology 32:4, pages 267-284.
Read now
JOHN HAYWARD. (2005) A General Model of Church Growth and Decline. The Journal of Mathematical Sociology 29:3, pages 177-207.
Read now

Articles from other publishers (32)

Alexander Medvedev & Oleg Kuzenkov. 2024. Mathematical Modeling and Supercomputer Technologies. Mathematical Modeling and Supercomputer Technologies 98 111 .
Stefano Scialla, Jens-Kristjan Liivand, Marco Patriarca & Els Heinsalu. (2023) A three-state language competition model including language learning and attrition. Frontiers in Complex Systems 1.
Crossref
D.A. Ammosov, S.P. Stepanov, A.A. Tyrylgin, N.V. Malysheva & L.S. Zamorshchikova. (2023) Partial learning using partially explicit discretization for multicontinuum/multiscale problems with limited observation: Language interactions simulation. Journal of Computational and Applied Mathematics 425, pages 115034.
Crossref
Martín Saavedra, Jorge Mira, Alberto P. Muñuzuri & Luís F. Seoane. (2023) A spectrum of complexity uncovers Dunbar’s number and other leaps in social structure. Chaos, Solitons & Fractals 170, pages 113389.
Crossref
D.A. Ammosov, A.V. Grigorev, S.P. Stepanov, N.V. Malysheva & L.S. Zamorshchikova. (2023) Numerical simulation of language interactions using online coupled Generalized Multiscale Finite Element Method. Journal of Computational and Applied Mathematics 423, pages 114962.
Crossref
Anne Kandler & Roman Unger. 2023. Diffusive Spreading in Nature, Technology and Society. Diffusive Spreading in Nature, Technology and Society 365 387 .
Luís F. Seoane & Jorge Mira. (2022) Are Dutch and French languages miscible?. The European Physical Journal Plus 137:7.
Crossref
Maria Díaz & Jennifer Switkes. (2021) Speaking out: A mathematical model of language preservation. Heliyon 7:5, pages e06975.
Crossref
Michael Boissonneault & Paul Vogt. (2021) A systematic and interdisciplinary review of mathematical models of language competition. Humanities and Social Sciences Communications 8:1.
Crossref
KUSHANI DE SILVA, ALADEEN BASHEER, KWADWO ANTWI-FORDJOUR, MATTHEW A. BEAUREGARD, VINEETA CHAND & RANA D. PARSHAD. (2021) THE “HIGHER” STATUS LANGUAGE DOES NOT ALWAYS WIN: THE FALL OF ENGLISH IN INDIA AND THE RISE OF HINDI. Advances in Complex Systems 23:08, pages 2050021.
Crossref
Marco Patriarca, Els Heinsalu & Jean Leó Leonard. 2020. Languages in Space and Time. Languages in Space and Time 179 196 .
Tessa Barrett-Walker, Michael J. Plank, Rachael Ka'ai-Mahuta, Daniel Hikuroa & Alex James. (2020) Kia kaua te reo e rite ki te moa, ka ngaro: do not let the language suffer the same fate as the moa. Journal of The Royal Society Interface 17:162, pages 20190526.
Crossref
Luís F. Seoane, Xaquín Loredo, Henrique Monteagudo & Jorge Mira. (2019) Is the coexistence of Catalan and Spanish possible in Catalonia?. Palgrave Communications 5:1.
Crossref
Mariamo Mussa Juane, Luis F. Seoane, Alberto P. Muñuzuri & Jorge Mira. (2019) Urbanity and the dynamics of language shift in Galicia. Nature Communications 10:1.
Crossref
John Wyburn & John Hayward. (2019) An application of an analogue of the partition function to the evolution of diglossia. Physica A: Statistical Mechanics and its Applications 516, pages 447-463.
Crossref
José Gómez-Aguilar & Abdon Atangana. (2018) Fractional Derivatives with the Power-Law and the Mittag–Leffler Kernel Applied to the Nonlinear Baggs–Freedman Model. Fractal and Fractional 2:1, pages 10.
Crossref
André Barreira da Silva Rocha. (2018) Social outcomes due to the interplay between language competition and ideology struggle. Physica A: Statistical Mechanics and its Applications 492, pages 1340-1351.
Crossref
Anne Kandler & Roman Unger. 2018. Diffusive Spreading in Nature, Technology and Society. Diffusive Spreading in Nature, Technology and Society 351 373 .
Y. Sofuoglu & N. Ozalp. (2015) Fractional Order Bilingualism Model Without Conversion from Dominant Unilingual Group to Bilingual Group. Differential Equations and Dynamical Systems 25:1, pages 1-9.
Crossref
R. Colucci, Jorge Mira, J. J. Nieto & M. V. Otero-Espinar. (2016) Non Trivial Coexistence Conditions for a Model of Language Competition Obtained by Bifurcation Theory. Acta Applicandae Mathematicae 146:1, pages 187-203.
Crossref
Adrián Carro, Raúl Toral & Maxi San Miguel. (2016) Coupled dynamics of node and link states in complex networks: a model for language competition. New Journal of Physics 18:11, pages 113056.
Crossref
Rana D. Parshad, Suman Bhowmick, Vineeta Chand, Nitu Kumari & Neha Sinha. (2016) What is India speaking? Exploring the “Hinglish” invasion. Physica A: Statistical Mechanics and its Applications 449, pages 375-389.
Crossref
E. HEINSALU, M. PATRIARCA & J. L. LÉONARD. (2014) THE ROLE OF BILINGUALS IN LANGUAGE COMPETITION. Advances in Complex Systems 17:01, pages 1450003.
Crossref
Menghan Zhang & Tao Gong. (2013) Principles of parametric estimation in modeling language competition. Proceedings of the National Academy of Sciences 110:24, pages 9698-9703.
Crossref
C. Bernard & S. Martin. (2012) Building strategies to ensure language coexistence in presence of bilingualism. Applied Mathematics and Computation 218:17, pages 8825-8841.
Crossref
Anne Kandler, Roman Unger & James Steele. (2010) Language shift, bilingualism and the future of Britain's Celtic languages. Philosophical Transactions of the Royal Society B: Biological Sciences 365:1559, pages 3855-3864.
Crossref
V. Sree Hari Rao & P. Raja Sekhara Rao. (2009) Dynamical models for the development of unilingual society into bilingual society. Differential Equations and Dynamical Systems 16:1-2, pages 29-45.
Crossref
H.M. El-Owaidy & M. Ismail. (2002) A mathematical model of bilingualism. Applied Mathematics and Computation 131:2-3, pages 415-432.
Crossref
. 1996. World Congress of Nonlinear Analysts '92. World Congress of Nonlinear Analysts '92 3227 3234 .
Carlos Castillo-Chavez, Jorge X. Velasco-Hernandez & Samuel Fridman. 1994. Frontiers in Mathematical Biology. Frontiers in Mathematical Biology 454 491 .
I. Baggs & H.I. Freedman. (1993) Can the speakers of a dominated language survive as unilinguals?: A mathematical model of bilingualism. Mathematical and Computer Modelling 18:6, pages 9-18.
Crossref
H. I. Freedman & I. Baggs. 1991. Differential Equations Models in Biology, Epidemiology and Ecology. Differential Equations Models in Biology, Epidemiology and Ecology 28 33 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.