This paper investigates the dynamical properties of a class of two-dimensional multiparameter Lotka–Volterra systems. We first employ the polynomial complete discrimination system theory to perform topological classification of the fixed point and analyze the stability of the system near the fixed point. Subsequently, we demonstrate that the system undergoes codimension-2 bifurcations, including 1:2 and 1:3 strong resonances, as well as weak resonance phenomena within Arnold tongues. Furthermore, we rigorously prove the existence of Marotto chaos through the identification of snap-back repellers under specific parameter regions. Finally, we provide extensive numerical simulations using Matlab R2023a and Maple 2023 to verify the theoretical results.
Chen et al. (Sat,) studied this question.
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