Some Models Of The Effect Of Impulsive Toxicant Input On Biological Populations

Motivated by the Ecotoxicology model established by T.G. Halam, this paper investigate in polluted environment a Logistic one population model with impulsive toxicant input and harvest, a Volterra predator-prey model with impulsive toxicant input and harvest, and a Volterra three-dimensional system with impulsive toxicant input with one predator population and two competitive prey with each other. The persistence of populations of these systems are concerned without taking into account the effect of populations on the toxicant concentration in the organism and environment, and assuming the toxicant amount input is fixed to the environment at each pulse moment. Some sufficient criteria on weak average persistence and extinction on the populations are obtained by the method of integral in mean. Especially, in the three populations model, three thresholds on the impulsive period are obtained. Furthermore, if the impulsive period is greater than the biggest threshold, all populations are weak average persistence; If the impulsive period lies between of the biggest threshold and the bigger, then two prey populations will be weak average persistence while the predator population extinct; If the period lies between of the bigger threshold and the smallest, prey population I is weak average persistence, prey population II and predator population extinct; If the period is less than the smallest threshold, all populations tend to extinction.