Stability and Bifurcation Analysis of Non-linear Ginzburg-Taneyhill Population Model with Minimal Maternal Quality

Mirela Garić Demirović; Dragana Kovačević

doi:10.5644/SJM.21.02.07

Authors

Mirela Garić Demirović University of Tuzla, Department of Mathematics, U. Vejzagića 4, Tuzla, Bosnia and Herzegovina https://orcid.org/0000-0001-9284-1891
Dragana Kovačević Department of Mathematics, University of Sarajevo, Zmaja od Bosne 33-35, Sarajevo, Bosnia and Herzegovina

DOI:

https://doi.org/10.5644/SJM.21.02.07

Keywords:

fixed point, Neimark-Sacker bifurcation, difference equations

Abstract

In this paper, we investigate the stability and Neimark-Sacker bifurcation of Ginzburg-Taneyhill model under the assumption of minimal maternal quality. The analysis begins with an examination of the existence and classification of equilibrium points, followed by a detailed study of their local stability. We show that the system undergoes a Neimark-Sacker bifurcation under certain parameter conditions, leading to the emergence of an invariant closed curve. Numerical simulations are presented to illustrate and confirm the theoretical results.

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