Bifurcation Analysis of a Discretized Prey-Predator System with Harvesting Effect on the Predator - Mokni, Karima; Fakhar, Rachid; Ch-Chaoui, Mohamed (Discontinuity, Nonlinearity, and Complexity, 2026)
We study the dynamic behavior of a discretized prey-predator system in this research. The model is formulated in terms of difference equations and derived by using the piecewise method, which takes into consideration the non-overlapping generations. The existence of fixed points as well as their local asymptotic stability are proved. Further, it is shown that the model experiences Neimark-Sacker bifurcation (NSB for short) and period-doubling bifurcation (PDB) in a small neighborhood of the coexistence fixed point under certain parametric conditions. This analysis utilizes bifurcation theory and the center manifold theorem. The chaos is stabilized using two different chaos control methods. Lastly, we verify our theoretical findings and provide more complex dynamics through computer analysis and numerical simulations.