Bifurcation Analysis of a Discrete Logistic System with Additive Allee Effect and Feedback Control

Nadia Agus Hadinata (University of Brawijaya)
Agus Suryanto (University of Brawijaya)
Wuryansari Muharini Kusumawinahyu (University of Brawijaya)

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

A discrete logistic system with addition Allee effect and feedback control is analyzed in this paper. The results of the analysis show that the model has a trivial fixed point and interior fixed point. The results of our stability analysis show that there are topological differences that depend on the step size. Bifurcation analysis is performed by using the center manifold theory and the bifurcation theorem. By taking the step size as a bifurcation parameter, we show that the model may go through a period-doubling and Neimark-Sacker bifurcations. Some numerical simulations are performed to confirm the result of the analysis.