SKM 2023 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 4: Poster
SOE 4.12: Poster
Montag, 27. März 2023, 17:00–19:00, P2/OG2
Delay Dynamics in a Nonlinear Economic Model — •Sándor Kovács1, Szilvia György1, Júlia Tompa2, and Noémi Gyúró2 — 1Department of Numerical Analysis, Eötvös LorándUniversity, \\ Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary\\ E-mail: alex@ludens.elte.hu — 2Eötvös Loránd University, \\ Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
This talk is about the qualitative behavior of an economic model proposed by D. Meyer (cf. [1]). It is shown that under certain conditions on the parameters the system has uniformly bounded and no non-trivial periodic solutions. Subsequently, a possible equilibrium on the boundary of the positive phase space not discussed in [1] was founded and showed that if there is no interior equilibrium, then the equilibrium at the boundary will become unstable, whereas the equilibrium at the boundary will be stable. In order to have more realism, two types of delay will be introduced: an infinite distributed delay and a discrete delay. It is shown that contrary to the result in [1] the distributed delay does not change the stability of the equilibrium points. Finally, by introducing a discrete delay, it was showed that at a certain parameter value Hopf bifurcation takes place: periodic solutions arise. [1] Meyer, D. Equity and Efficiency in Regional Policy. Periodica Mathematica Hungarica Vol. 56 (1), 2008, 105*119.