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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.

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.

Abstract:Taking into account stage-structure for prey and periodic pulse at different fixed moments, a delayed prey-predator system with Beddington-type functional response was investigated. Applying the small amplitude perturbation method and Floquet's theory, we obtained the sufficient conditions for the local stability, globally asymptotical stability and global attractivity of the prey-extinction periodic solution. Further, by using theories of impulsive differential equation and delay differential equation, we obtained the conditions of the permanence of this system. Finally, examples and numerical simulations are given to show the complex dynamic behaviours of the system. Especially, we find that the impulsive and the time delay play an important role in the permanence of the system.

This report describes the surveillance over the past 8 years of carbon monoxide (CO) levels in a factory producing gas from coal. Where workers were working in areas of the factory where the air might be polluted by CO we found that measurement of carboxyhaemoglobin (HbCO) levels in their blood was a sufficiently sensitive test of exposure. Measurements on samples taken before and after a shift showed a significant difference. Our measurements of a HbCO blank control in two normal population groups was very close to the biological limit value of that for normal groups in the USA and Germany.