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An impulsive two-prey and one-predator model with square root functional responses, mutual interference, and integrated pest management is constructed. By using techniques of impulsive perturbations, comparison theorem, and Floquet theory, the existence and global asymptotic stability of prey-eradication periodic solution are investigated. We use some methods and sufficient conditions to prove the permanence of the system which involve multiple Lyapunov functions and differential comparison theorem. Numerical simulations are given to portray the complex behaviors of this system. Finally, we analyze the biological meanings of these results and give some suggestions for feasible control strategies.

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Taking into account that individual organisms usually go through immature and mature stages, in this paper, we investigate the dynamics of an impulsive prey-predator system with a Holling II functional response and stage-structure. Applying the comparison theorem and some analysis techniques, the sufficient conditions of the global attractivity of a mature predator periodic solution and the permanence are investigated. Examples and numerical simulations are shown to verify the validity of our results.

Based on the biological resource management of natural resources, a stage-structured predator-prey model with Holling type III functional response, birth pulse, and impulsive harvesting at different moments is proposed in this paper. By applying comparison theorem and some analysis techniques, the global attractivity of predator-extinction periodic solution and the permanence of this system are studied. At last, examples and numerical simulations are given to verify the validity of the main results.