Role of induced volatile emission modelling tritrophic interaction (Q2155480)

Herbivore induced plant volatiles (HIPVs) are specific volatile organic compounds (VOC) produced by plants in response to herbivory. Some HIPVs are produced only after damage but even intact plants produce lower quantities of HIPVs. The paper under review addresses the role of VOC in a plant-herbivore-carnivore system whose dynamics is described by the Rosenzweig-MacArthur model with three ordinary differential equations. The authors assume that VOC are emitted from damaged parts of the plants, as well as from intact plants and the neighboring plants. Positivity and boundedness of solutions to the system are studied first, followed by the analysis of the stability of the three critical points, the trivial equilibrium \(E_{0}=\left( 0,0,0\right)\), axial equilibrium \(E_{1}=\left( K,0,0\right)\), and the interior equilibrium \(E_{\ast}\). Routh-Hurwitz criterion and Lyapunov direct method are used respectively to establish local (Theorem 1) and global (Theorem 2) asymptotic stability of \(E_{\ast}\). Bifurcation analysis reveals transcritical bifurcation at \(E_{1}\) (Theorem 4) and a saddle-node and Hopf bifurcations at \(E_{\ast}\) (Theorems 5 and 6 respectively). In the final part of the paper, theoretical results are illustrated with the numerical simulations.