Effects of limited volatiles release by plants in tritrophic interactions

We introduce a mathematical model to describe the tritrophic interaction between crop,pest and the pest natural enemy where the release of Volatile Organic Compounds (VOCs) by crop istaken into account. The VOCs may be considered as an indirect defence mechanism of the plant asthey attract the pest natural enemies toward the attacked plants. The model dynamics is studied throughqualitative analysis and numerical simulations. The factors that may enhance pest disappearance areidentified. In particular, we show that VOCs may have a beneficial effect on the environment sincetheir release may be able to stabilize the model dynamics. Specifically, for the parameter values thatwe have explored, this effect can arise only when both the phenomena of VOCs basic plant release andVOCs plant release due to pest attack are present.