Abstract
This paper examines the discrete-time Rosenzweig-MacArthur predator–prey model featuring a general predator functional response. We determine the closed and positively invariant set D, where the system’s dynamics are analyzed. The set contains extinction, boundary, and interior equilibrium points, which we explore in detail. Our research shows that extinction and boundary equilibrium points can be globally asymptotically stable. We observe transcritical and period-doubling at the boundary equilibrium point with stable two-cycle bifurcation. During period-doubling bifurcation at the boundary equilibrium, one Lyapunov exponent is zero, while the other is negative. The interior equilibrium point exhibits Neimark-Sacker and period-doubling bifurcation with unstable two-cycle. For the Neimark-Sacker bifurcation, we provide an exact form of the first Lyapunov exponent. Our research also shows that the system is permanent in set D. Finally, we apply our theoretical findings to various well-known predator functional responses.
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Bešo, E., Kalabušić, S. & Pilav, E. Dynamics of the discrete-time Rosenzweig-MacArthur predator–prey system in the closed positively invariant set. Comp. Appl. Math. 42, 341 (2023). https://doi.org/10.1007/s40314-023-02481-w
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DOI: https://doi.org/10.1007/s40314-023-02481-w