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• W2892288425 abstract "In this paper, we consider the complex dynamics of a discrete predator–prey system with a strong Allee effect on the prey and a ratio-dependent functional response, which is the discrete version of the continuous system in (Nonlinear Anal., Real World Appl. 16:235–249, 2014). First, by giving several examples to display the limitations and errors of the local stability of the equilibrium point p obtained in (Nonlinear Anal., Real World Appl. 16:235–249, 2014), we provide an easily verified and complete discrimination criterion for the local stability of this equilibrium. Then we study some properties of its discrete version, especially for the stability and bifurcation for the equilibrium point $E_{1}$ , which has not been considered in any literature to the best of our knowledge. By using the center manifold theorem and bifurcation theory, we consider the flip bifurcation of this system at $E_{1}$ and obtain the stability of the closed orbits bifurcated from $E_{1}$ . The numerical simulations not only show the correctness of our theoretical analysis, but also we find some new and interesting dynamics of this system." @default.
• W2892288425 created "2018-09-27" @default.
• W2892288425 creator A5038462889 @default.
• W2892288425 creator A5086943373 @default.
• W2892288425 date "2018-09-12" @default.
• W2892288425 modified "2023-10-13" @default.
• W2892288425 title "Complex dynamics of a discrete predator–prey system with a strong Allee effect on the prey and a ratio-dependent functional response" @default.
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• W2892288425 doi "https://doi.org/10.1186/s13662-018-1781-x" @default.
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