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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 4: Poster

SOE 4.12: Poster

Monday, March 27, 2023, 17:00–19:00, P2/OG2

Delay Dynamics in a Nonlinear Economic Model — •Sándor Kovács1, Szilvia György1, Júlia Tompa2, and Noémi Gyúró21Department 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.

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