A generalized diffusive IS-LM business cycle model with delays in gross product and capital stock

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dc.citation.epage480
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та обчислення
dc.citation.spage470
dc.citation.volume11
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.authorХаттаф, К.
dc.contributor.authorЮсфі, Н.
dc.contributor.authorElkarmouchi, M.
dc.contributor.authorHattaf, K.
dc.contributor.authorYousfi, N.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-10-20T08:10:19Z
dc.date.created2024-02-27
dc.date.issued2024-02-27
dc.description.abstractУ статті пропонується модель бізнес-циклу IS-LM із дифузійним і відстроченим процесом із відсотковою ставкою, загальними інвестиціями та пропозицією грошей за однорідних граничних умов Неймана. Часові затримки відповідно включені до основного капіталу та валового продукту. Спочатку продемонстровано обґрунтування математичної та економічної моделі. Шляхом дослідження відповідного характеристичного рівняння доведено локальну стійкість економічної рівноваги та існування біфуркації Хопфа.
dc.description.abstractIn this paper, we suggest a diffusive and delayed IS-LM business cycle model with interest rate, general investment and money supply under homogeneous Neumann boundary conditions. The time delays are respectively incorporated into capital stock and gross product. We first demonstrate the model’s sound mathematical and economic posing. By examining the corresponding characteristic equation, the local stability of the economic equilibrium and the existence of Hopf bifurcation are proved.
dc.format.extent470-480
dc.format.pages11
dc.identifier.citationElkarmouchi M. A generalized diffusive IS-LM business cycle model with delays in gross product and capital stock / M. Elkarmouchi, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 470–480.
dc.identifier.citationenElkarmouchi M. A generalized diffusive IS-LM business cycle model with delays in gross product and capital stock / M. Elkarmouchi, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 470–480.
dc.identifier.doidoi.org/10.23939/mmc2024.02.470
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/113807
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та обчислення, 2 (11), 2024
dc.relation.ispartofMathematical Modeling and Computing, 2 (11), 2024
dc.relation.references[1] Elkarmouchi M., Lasfar S., Hattaf Kh., Yousfi N. Spatiotemporal dynamics of a delayed IS-LM model with interest rate and general investment function. Journal of Mathematics and Computer Science. 31 (1), 70–80 (2023).
dc.relation.references[2] Hattaf K., Riad D., Yousfi N. A generalized business cycle model with delays in gross product and capital stock. Chaos, Solitons & Fractals. 98, 31–37 (2017).
dc.relation.references[3] 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[4] Riad D., Hattaf K., Yousfi N. Mathematical analysis of a delayed IS-LM model with general investmentfunction. The Journal of Analysis. 27 (4), 1047–1064 (2019).
dc.relation.references[5] 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[6] Zhou L., Li Y. A generalized dynamic IS-LM model with delayed time in investment processes. Applied Mathematics and Computation. 196 (2), 774–781 (2008).
dc.relation.references[7] Cesare L. D., Sportelli M. A dynamic IS-LM model with delayed taxation revenues. Chaos Solitons & Fractals. 25 (1), 233–244 (2005).
dc.relation.references[8] Sportelli M., Cesare L. D., Binetti M. T. A dynamic IS-LM model with two time delays in public sector. Applied Mathematics and Computation. 243, 728–739 (2014).
dc.relation.references[9] Akanksha R., Bhatia S. K., Hiremath K. R. Inspecting the stability of non-linear IS-LM model with dual time delay. Chaos, Solitons & Fractals. 165 (2), 112821 (2022).
dc.relation.references[10] 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[11] Hale J. Theory of Functional Differential Equations. Springer–Verlag, Heidelberg (1977).
dc.relation.references[12] Ruan S., Wei J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous Discrete and Impulsive Systems Series A. Mathematical Analysis. 10, 863–874 (2003).
dc.relation.referencesen[1] Elkarmouchi M., Lasfar S., Hattaf Kh., Yousfi N. Spatiotemporal dynamics of a delayed IS-LM model with interest rate and general investment function. Journal of Mathematics and Computer Science. 31 (1), 70–80 (2023).
dc.relation.referencesen[2] Hattaf K., Riad D., Yousfi N. A generalized business cycle model with delays in gross product and capital stock. Chaos, Solitons & Fractals. 98, 31–37 (2017).
dc.relation.referencesen[3] 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[4] Riad D., Hattaf K., Yousfi N. Mathematical analysis of a delayed IS-LM model with general investmentfunction. The Journal of Analysis. 27 (4), 1047–1064 (2019).
dc.relation.referencesen[5] 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[6] Zhou L., Li Y. A generalized dynamic IS-LM model with delayed time in investment processes. Applied Mathematics and Computation. 196 (2), 774–781 (2008).
dc.relation.referencesen[7] Cesare L. D., Sportelli M. A dynamic IS-LM model with delayed taxation revenues. Chaos Solitons & Fractals. 25 (1), 233–244 (2005).
dc.relation.referencesen[8] Sportelli M., Cesare L. D., Binetti M. T. A dynamic IS-LM model with two time delays in public sector. Applied Mathematics and Computation. 243, 728–739 (2014).
dc.relation.referencesen[9] Akanksha R., Bhatia S. K., Hiremath K. R. Inspecting the stability of non-linear IS-LM model with dual time delay. Chaos, Solitons & Fractals. 165 (2), 112821 (2022).
dc.relation.referencesen[10] 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[11] Hale J. Theory of Functional Differential Equations. Springer–Verlag, Heidelberg (1977).
dc.relation.referencesen[12] Ruan S., Wei J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous Discrete and Impulsive Systems Series A. Mathematical Analysis. 10, 863–874 (2003).
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.subjectекономіка
dc.subjectдифузія
dc.subjectстабільність
dc.subjectзатримки часу
dc.subjectбіфуркація Хопфа
dc.subjecteconomics
dc.subjectdiffusion
dc.subjectstability
dc.subjecttime delays
dc.subjectHopf bifurcation
dc.titleA generalized diffusive IS-LM business cycle model with delays in gross product and capital stock
dc.title.alternativeУзагальнена дифузійна модель бізнес-циклу IS-LM із затримками валового продукту та капіталу
dc.typeArticle

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Mathematical Modeling And Computing. – 2024. – Vol. 11, No. 2