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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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In this paper, we build a multispecies predator-prey model with mutual interference and time delays. By means of the comparison theorem, Ascoli theorem and Lebesgue dominated convergence theorem, we establish the sufficient conditions of permanence and investigate the existence of a unique almost periodic solution. By constructing a suitable Lyapunov function, we obtain that the positive almost periodic solution is globally attractive. Finally, we give numerical simulations to indicate the complex dynamical behaviors of this system.

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An impulsive one-predator and two-prey system with stage-structure and generalized functional response is proposed and analyzed. By reasonable assumption and theoretical analysis, we obtain conditions for the existence and global attractivity of the predatorextinction periodic solution. Sufficient conditions for the permanence of this system are established via impulsive differential comparison theorem. Furthermore, abundant results of numerical simulations are given by choosing two different and concrete functional responses, which indicate that impulsive effects, stage-structure, and functional responses are vital to the dynamical properties of this system. Finally, the biological meanings of the main results and some control strategies are given.

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In this paper, a delayed Gompertz model with Holling-IV type function response and impulsive effects at different moment on the prey is proposed. By using impulsive comparison theorem, the stroboscopic mapping and some analysis techniques, the existence and global attractivity of the predator-extinction periodic solution are investigated. Sufficient conditions of the permanence of this system are also obtained. Examples and numerical simulations are shown to verify the validity of our results.