Dynamic complexities in a pest control model with birth pulse and harvesting

Abstract

In this paper, an impulsive model is discussed for an integrated pest management approach comprising of chemical and mechanical controls. The pesticides and harvesting are used to control the stage-structured pest population. The mature pest give birth to immature pest in pulses at regular intervals. The pest is controlled by spraying chemical pesticides affecting immature as well as mature pest. The harvesting of both immature and mature pest further reduce the pest population. The discrete dynamical system obtained from stroboscopic map is analyzed. The threshold conditions for stability of pest-free state as well as non-trivial period-1 solution is obtained. The effect of pesticide spray timing and harvesting on immature as well as mature pest are shown. Finally, by numerical simulation with MATLAB, the dynamical behaviors of the model is found to be complex. Above the threshold level there is a characteristic sequence of bifurcations leading to chaotic dynamics. Route to chaos is found to be period-doubling. Period halving bifurcations are also observed.