Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand
An analysis of dynamics of demand-inventory model with stock-level-dependent demand formulated as a three-dimensional system of difference equations with four parameters is considered. By reducing the model to the planar system with five parameters, an analysis of one-parameter bifurcation of equili...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/8162865 |
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| _version_ | 1850170245003608064 |
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| author | Piotr Hachuła Magdalena Nockowska-Rosiak Ewa Schmeidel |
| author_facet | Piotr Hachuła Magdalena Nockowska-Rosiak Ewa Schmeidel |
| author_sort | Piotr Hachuła |
| collection | DOAJ |
| description | An analysis of dynamics of demand-inventory model with stock-level-dependent demand formulated as a three-dimensional system of difference equations with four parameters is considered. By reducing the model to the planar system with five parameters, an analysis of one-parameter bifurcation of equilibrium points is presented. By the analytical method, we prove that nondegeneracy conditions for the existence of Neimark-Sacker bifurcation for the planar system are fulfilled. To check the sign of the first Lyapunov coefficient of Neimark-Sacker bifurcation, we use numerical simulations. We give phase portraits of the planar system to confirm the previous analytical results and show new interesting complex dynamical behaviours emerging in it. Finally, the economical interpretation of the system is given. |
| format | Article |
| id | doaj-art-a34e0e93238441c9a2ecfdb6a2adff7f |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a34e0e93238441c9a2ecfdb6a2adff7f2025-08-20T02:20:32ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/81628658162865Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent DemandPiotr Hachuła0Magdalena Nockowska-Rosiak1Ewa Schmeidel2Institute of Logistics and Warehousing, Poznań, PolandLodz University of Technology, Łódź, PolandUniversity of Białystok, Białystok, PolandAn analysis of dynamics of demand-inventory model with stock-level-dependent demand formulated as a three-dimensional system of difference equations with four parameters is considered. By reducing the model to the planar system with five parameters, an analysis of one-parameter bifurcation of equilibrium points is presented. By the analytical method, we prove that nondegeneracy conditions for the existence of Neimark-Sacker bifurcation for the planar system are fulfilled. To check the sign of the first Lyapunov coefficient of Neimark-Sacker bifurcation, we use numerical simulations. We give phase portraits of the planar system to confirm the previous analytical results and show new interesting complex dynamical behaviours emerging in it. Finally, the economical interpretation of the system is given.http://dx.doi.org/10.1155/2017/8162865 |
| spellingShingle | Piotr Hachuła Magdalena Nockowska-Rosiak Ewa Schmeidel Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand Discrete Dynamics in Nature and Society |
| title | Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand |
| title_full | Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand |
| title_fullStr | Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand |
| title_full_unstemmed | Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand |
| title_short | Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand |
| title_sort | neimark sacker bifurcation in demand inventory model with stock level dependent demand |
| url | http://dx.doi.org/10.1155/2017/8162865 |
| work_keys_str_mv | AT piotrhachuła neimarksackerbifurcationindemandinventorymodelwithstockleveldependentdemand AT magdalenanockowskarosiak neimarksackerbifurcationindemandinventorymodelwithstockleveldependentdemand AT ewaschmeidel neimarksackerbifurcationindemandinventorymodelwithstockleveldependentdemand |