Multistability and chaos induced by discrete dynamics with variable carrying capacity and wind effect: A comparative analysis in discrete and continuous predator–prey models

This article presents an investigation of predator-prey interaction through both continuous and discrete models, emphasizing the roles of variable carrying capacity and wind effect. In the continuous model, we analyze the existence and local stability of equilibria, identifying Hopf and transcritical bifurcations. Meanwhile, for the discrete model, we also examine the stability of fixed points and reveal bifurcation phenomena, including Flip and Neimark-Sacker bifurcations. Notably, in numerical simulations, specific periodic structures-Arnold tongues and shrimp-shaped patterns-often arise within chaotic regions. Through the bi-parameter analysis, we further demonstrate complex dynamical behaviors such as period-bubbling and coexistence of multiple attractors. Finally, the findings reveal marked sensitivity of population densities to initial conditions.