Dynamical analysis, optimum control and pattern formation in the biological pest (EFSB) control model

Abstract

• Development of model of eggplant fruit and shoot borer in reference to egg plant-parasatoid interaction. • Local stability and local bifurcation analysis for the equilibrium points. • Global stability analysis using graph theoretic method and optimization through linear feedback control. • Development of Spatio-temporal biological pest control system and considered feasible framework of pattern formation in it. Prevention of crops from pest has always been a serious cause of concern throughout the world, especially in agricultural countries as it contributes majorly to the economy of these countries. Keeping in mind this issue, we have formulated a mathematical model of Eggplant fruit and shoot borer which has been controlled through biological control. The dynamical analysis of the system has been discussed which includes the boundedness and positivity of the system. Local stability analysis of the system is discussed followed by local bifurcation analysis of each steady state solutions.The global stability analysis of non-trivial is done by graph theoretic approach by constructing a Lyapunov function. The optimization of the biological control strategy has also been discussed using linear feedback control. Further, we have also proposed a Spatio-temporal model and investigated it to observe the evolution of diffusive pattern in a biological pest control model. The reason of discussing the Spatio-temporal model is to focus on how diffusion can also be a method to control the pest population. The numerical simulation has been discussed to validate our analytical results obtained. Finally, we have also obtained the global sensitivity analysis using LHS method for U , x 2 and x 3 .