A mathematical model study on plant root pest management

Unlike conventional methods of pests control, introducing in an appropriate mathematical model can contribute a batter performance on pests control with higher efficiency while lest damage to ecosystem. To fill the research gap on plant root pest control, we propose a plant root pest management model with state pulse feedback control. Firstly, the stability of the equilibrium point of the model (1.3) is analyzed by using the linear approximate equation, given that the only positive equilibrium point of model (1.3) is globally asymptotically stable. Moreover, the existence and uniqueness of order 1 periodic solutions of model (1.3) are discussed in detail according to the geometric theory of semi-continuous dynamical systems, successor functions method and the qualitative theory of differential equations. Finally, with further analysis in different methods, the asymptotic stability of the order 1 periodic solution of model (1.3) is obtained by using Similar Poincare Criterion or interval set theorem. The results show that this model can effectively control the number of pests below the economic level of damage.