Mathematical analysis of a spatiotemporal dynamics of a delayed IS-LM model in economics

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dc.citation.epage202
dc.citation.issue11
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage189
dc.citation.volume1
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationРегіональний центр освіти і підготовки професій (CRMEF)
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.affiliationCentre R´egional des M´etiers de l’Education et de la Formation (CRMEF)
dc.contributor.authorЕлькармучі, М.
dc.contributor.authorЛасфар, С.
dc.contributor.authorХаттаф, К.
dc.contributor.authorЮсфі, Н.
dc.contributor.authorElkarmouchi, M.
dc.contributor.authorLasfar, S.
dc.contributor.authorHattaf, K.
dc.contributor.authorYousfi, N.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-10-20T07:44:12Z
dc.date.created2024-02-24
dc.date.issued2024-02-24
dc.description.abstractМета цього дослідження полягає в тому, щоб запропонувати та проаналізувати просторово-часову модель IS-LM із двома затримками: процентною ставкою, перевагою ліквідності та загальною інвестиційною функцією. Перша затримка в запропонованій моделі відноситься до часової затримки між рішенням про інвестиції та його реалізацією. Але друга це затримка інвестиційного виробництва. Доведено коректність моделі. Здійснено аналіз стійкості та існування біфуркації Хопфа. Крім того, наведено числові приклади, які підтверджують аналітичні результати.
dc.description.abstractThe purpose of this research is to suggest and analyze a spatiotemporal of an IS-LM model with two delays, interest rate, liquidity preference and general investment function. The first delay into the proposed model refers to the time delay between the decision of investment and his implementation. However, the second one represents the delay in investment production. The well posedness of the model is proved. The stability analysis and the existence of Hopf bifurcation are obtained. Furthermore, numerical examples that confirm the analytical results are shown.
dc.format.extent189-202
dc.format.pages14
dc.identifier.citationMathematical analysis of a spatiotemporal dynamics of a delayed IS-LM model in economics / M. Elkarmouchi, S. Lasfar, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 189–202.
dc.identifier.citationenMathematical analysis of a spatiotemporal dynamics of a delayed IS-LM model in economics / M. Elkarmouchi, S. Lasfar, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 189–202.
dc.identifier.doi10.23939/mmc2024.01.189
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/113778
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 11 (1), 2024
dc.relation.ispartofMathematical Modeling and Computing, 11 (1), 2024
dc.relation.references[1] Cai J. P. Hopf bifurcation in the IS-LM business cycle model with time delay. Electronic Journal of Differential Equations. 2005, 15 (2005).
dc.relation.references[2] Hattaf K., Riad D., Yousfi N. A generalized business cycle model with delays in grossn product and capital stock. Chaos, Solitons & Fractals. 98, 31–37 (2017).
dc.relation.references[3] Riad D., Hattaf K., Yousfi N. Mathematical analysis of a delayed IS-LM model with general investment function. The Journal of Analysis. 27 (4), 1047–1064 (2019).
dc.relation.references[4] Hu W., Zhao H., Dong T. Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect. Complexity. 2018, 1263602 (2018).
dc.relation.references[5] Riad D., Hattaf K., Yousfi N. Dynamics of a delayed business cycle model with general investment function. Chaos, Solitons & Fractals. 85, 110–119 (2016).
dc.relation.references[6] Hattaf K., Yousfi N. A generalized HBV model with diffusion and two delays. Computers & Mathematics with Applications. 69 (1), 31–40 (2015).
dc.relation.references[7] Hattaf K. Spatiotemporal dynamics of a generalized viral infection model with distributed delays and CTL immune response. Computation. 7 (2), 21 (2019).
dc.relation.references[8] Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, Springer-Verlag (1993).
dc.relation.references[9] Kuang Y. Delay Differential Equations with Applications in Population Dynamics. Academic Press, New York (1993).
dc.relation.references[10] Hale J. Theory of Functional Differential Equations. Springer-Verlag, Heidelberg (1977).
dc.relation.references[11] Ruan S., Wei J. On the zeros of transcendental functions with applications to stability of delay differetial equantions with two delays. Dynamics of Continuous, Discrete and Impulsive Systems. Series A. 10, 863–874 (2003).
dc.relation.referencesen[1] Cai J. P. Hopf bifurcation in the IS-LM business cycle model with time delay. Electronic Journal of Differential Equations. 2005, 15 (2005).
dc.relation.referencesen[2] Hattaf K., Riad D., Yousfi N. A generalized business cycle model with delays in grossn product and capital stock. Chaos, Solitons & Fractals. 98, 31–37 (2017).
dc.relation.referencesen[3] Riad D., Hattaf K., Yousfi N. Mathematical analysis of a delayed IS-LM model with general investment function. The Journal of Analysis. 27 (4), 1047–1064 (2019).
dc.relation.referencesen[4] Hu W., Zhao H., Dong T. Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect. Complexity. 2018, 1263602 (2018).
dc.relation.referencesen[5] Riad D., Hattaf K., Yousfi N. Dynamics of a delayed business cycle model with general investment function. Chaos, Solitons & Fractals. 85, 110–119 (2016).
dc.relation.referencesen[6] Hattaf K., Yousfi N. A generalized HBV model with diffusion and two delays. Computers & Mathematics with Applications. 69 (1), 31–40 (2015).
dc.relation.referencesen[7] Hattaf K. Spatiotemporal dynamics of a generalized viral infection model with distributed delays and CTL immune response. Computation. 7 (2), 21 (2019).
dc.relation.referencesen[8] Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, Springer-Verlag (1993).
dc.relation.referencesen[9] Kuang Y. Delay Differential Equations with Applications in Population Dynamics. Academic Press, New York (1993).
dc.relation.referencesen[10] Hale J. Theory of Functional Differential Equations. Springer-Verlag, Heidelberg (1977).
dc.relation.referencesen[11] Ruan S., Wei J. On the zeros of transcendental functions with applications to stability of delay differetial equantions with two delays. Dynamics of Continuous, Discrete and Impulsive Systems. Series A. 10, 863–874 (2003).
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.subjectекономіка
dc.subjectмодель IS-LM
dc.subjectчасові затримки
dc.subjectасимптотична стійкість
dc.subjectдифузія
dc.subjectбіфуркація Хопфа
dc.subjecteconomics
dc.subjectIS-LM model
dc.subjecttime delays
dc.subjectasymptotic stability
dc.subjectdiffusion
dc.subjectHopf bifurcation
dc.titleMathematical analysis of a spatiotemporal dynamics of a delayed IS-LM model in economics
dc.title.alternativeМатематичний аналіз просторово-часової динаміки відстроченої моделі IS-LM в економіці
dc.typeArticle

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Mathematical Modeling And Computing. – 2024. – Vol. 11, No. 1