Impulse lethal control and contraception control of seasonal breeding rodent

The rodent is one important component of an ecosystem; however, abundance of rodents may have negative effects to humans. Based on a seasonally breeding model and the logistic model, the effect of impulse lethal control and impulse contraception control on rodent population dynamics is investigated. The existence and stability of the periodic solution were analyzed. The condition of rodent population dying out is the same for lethal and contraception control. However, the process of rodent population tending to a stable periodic solution is different obviously. Under lethal control, the rodent population tends to a stable periodic solution more quickly, whereas under contraception control, the rodent population develops slowly.