Bifurcations and Marotto’s chaos of a discrete Lotka–Volterra predator–prey model

Abstract

This paper mainly studied the qualitative properties of a four-parameter discrete Lotka–Volterra predator–prey model. By applying polynomial algebraic theory to solve complex high-order semi-algebraic systems, and combining bifurcation theory, we provided not only the topological structure of orbits in the vicinity of each fixed point, but also the specific parameter conditions that give rise to codimension one and codimension two bifurcations of the model including transcritical, flip, Neimark–Sacker bifurcations, strong resonances of 1:2, 1:3, 1:4, and weak resonance Arnold tongue. Besides, we also discussed the chaotic behavior in the sense of Marotto of the model. Finally, employing Maple 2023 and Matlab R2019a, we conducted numerical simulations of the dynamic behavior of the model to further verify the aforementioned theoretical results.