Abstract
In this paper, an impulsive system of differential equations is proposed to model a pest control system. The stage-structured system consists of immature and mature pest population. Birth pulses occur at regular intervals to release immature pest. The pest is controlled by spraying chemical pesticides affecting both immature and mature pest. The stroboscopic map of the impulsive system is analyzed for the stability of pest-free and non-trivial period-1 solution. Numerical simulations with MATLAB reveal the complex dynamical behavior. Period doubling cascade, chaos and period halving bifurcations are observed above the threshold level.
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