The dynamics of a stage-structured pest management system is studied by means of autonomous piecewise linear systems with impulses governed by state feedback control. The sufficient conditions of existence and stability of periodic solutions are obtained by means of the sequence convergence rule and the analogue of the Poincare criterion. The attractive region of periodic solutions is investigated theoretically by qualitative analysis. The bifurcation diagrams of periodic solutions are obtained by using the Poincare map, as well as the chaotic solution generated via a cascade of period-doubling bifurcations. The superiority of the state feedback control strategy is also discussed.
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Jiang et al. (2005) studied this question.