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In this article, a singular perturbation is introduced to analyze the global asymptotic stability of positive equilibria of ratio-dependent predator-prey models with stage structure for the prey. We prove theoretical results and show numerically that the proposed approach is feasible and efficient.
According to the economic and biological aspects of renewable resources management, we propose a Lotka-Volterra predator-prey model with state dependent impulsive harvest. By using the Poincaré map, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order… (More)