The Modified Palomba Economic Model by Difference Equations and its Stability Analysis
In this study, Palomba economic model was analyzed through difference equations. For these products given as capital and consumer goods in the model, their non-marketable loss rates were also taken into account. Tirivial and non-tirivial equilibrium points were found and local asymptotic stability (LAS) conditions of these equilibrium points were investigated. Although the non-trivial equilibrium point is always unstable, the conditions for the stability of the trivial equilibrium point were found. In this way, in addition to the thought put forward by Palomba, the absence of periodicity was expressed too. The findings were supported by numerical studies.
Keywords:
Palomba Economic Model, Difference Equation System, Mathematical Model Stability Analysis,
___
- Daşbaşı, B., Daşbaşı, T., Doğrusal Programlama Minimizasyon Problemi İçin Matematiksel Model Ve Uygulaması: Kimyasal Gübre Alımı, The Journal of International Social Research, 10(50), 675-683, 2017.
- Mondal, S.P., Khan, N.A., Vishwakarma, D., Saha, A.K., Existence and Stability of Difference Equation in Imprecise Enviroment, Nonlinear Engineering, 7(4), 263-271, 2018.
- Harvie, D., Kelmanson, M.A., Knapp, D.G., A Dynamical Model of Business Cycle Asymmetries: Extending Goodwin, Economic, 12, 53–92, 2007.
- Gandolfo, G., Giuseppe Palomba and the Lotka-Volterra Equations, Rendiconti Lincei, 19(4), 347-357, 2008.
- Daşbaşı, B., Boztosun, D., Çoklu Kesirli Mertebeden Diferansiyel Denklemler ile Palomba Ekonomi Modelinin Kararlılık Analizi, Journal of International Social Research, 11(59), 901-907, 2018.
- Elaydi, S.N., An Introduction To Difference Equations, Third Edition ed., Springer, 2005.
- Allen, L.J.S., An Introduction to Mathematical Biology., 2007, ISBN 10: 0-13-035216-0.
- Fulford, G., Forrester, P., Jones, A., Modelling with Differential and Difference Equations (Australian Mathematical Society Lecture Series Book 10), 1st ed. U.K., Cambridge University Press, 2001 (Reprinted).
- Mickens, R.E., Difference equations: theory, applications and advanced topics, Third Edition ed., CRC Press, 2015.
- Başlangıç: 2009
- Yayıncı: Akdeniz Üniversitesi