Bifurcations and chaotic behavior of a predator-prey model with discrete time

Abstract

<abstract><p>In this paper, the dynamical behavior of a predator-prey model with discrete time is discussed in terms of both theoretical analysis and numerical simulation. The existence and stability of four equilibria are analyzed. It is proved that the system undergoes Flip bifurcation and Hopf bifurcation around its unique positive equilibrium point using center manifold theorem and bifurcation theory. Additionally, by applying small perturbations to the bifurcation parameter, chaotic cases occur at some corresponding internal equilibria. Finally, numerical simulations are provided with the help of maximum Lyapunov exponent and phase diagrams, which reveal a complex dynamical behavior.</p></abstract>

Analysis of the Dynamical Properties of Discrete Predator‐Prey Systems with Fear Effects and Refuges

“…By focusing on the system of equations at W c (0, 0), we can derive the following outcome: Based on the reference [33], it is stated that when considering values at (N, P, δ) � (0, 0, 0) and having θ 1 ≠ 0, θ 2 ≠ 0, the system exhibits a fip bifurcation at the fxed point N * (x * , y * ). If θ 2 > 0( < 0), the point with a period of 2 is stable (unstable).…”