Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand

Hachuła, Piotr; Nockowska-Rosiak, Magdalena; Schmeidel, Ewa

Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand

Abstract

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.

Keywords

stock inventory inventory management modelling

zapasy zarządzanie zapasami modelowanie

Citation

Piotr Hachuła, Magdalena Nockowska-Rosiak, and Ewa Schmeidel, “Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand,” Discrete Dynamics in Nature and Society, vol. 2017, Article ID 8162865, 10 pages, 2017. https://doi.org/10.1155/2017/8162865

URI

https://depot.ceon.pl/handle/123456789/16026

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