## Weak average persistence and extinction of a predator-prey system in a polluted environment with impulsive toxicant input.(English)Zbl 1133.92032

Summary: We investigated a predator-prey system in a polluted environment with impulsive toxicant input at fixed moments. We obtained two thresholds on the impulsive period by assuming the toxicant amount input is fixed to the environment at each pulse moment. If the impulsive period is greater than the big threshold, then both populations are weakly average persistent. If the period lies between of the two thresholds, then the prey population will be weakly average persistent while the predator population goes extinct. If the period is less than the small threshold, both populations tend to extinction. Finally, our theoretical results are confirmed by own numerical simulations.

### MSC:

 92D40 Ecology 34A37 Ordinary differential equations with impulses 34C60 Qualitative investigation and simulation of ordinary differential equation models
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### References:

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