BISTABILITY, GENERALIZED AND ZERO-HOPF BIFURCATIONS IN A PEST CONTROL MODEL WITH FARMING AWARENESS

Abstract

Introduction of biopesticides and predators in the crop fields has a crucial impact on the pest management as the biopesticides induce infection among the pest population and the infected pests are easy to be captured by the predators. In this paper, we investigate a mathematical model for a pest management system with farming awareness-based inclusion of predators and biopesticides. The level of awareness among the farmers is assumed to grow at a constant rate besides its growth due to an increase in the pest population in the crop field. The proposed model is analyzed mathematically for the feasibility and stability of the equilibrium points; existence of Hopf bifurcation together with direction and stability of the bifurcating periodic solutions are discussed; sufficient conditions are derived for which the system does not exhibit any periodic solution. Our simulation results show that the activeness of farmers for employing biopesticides in the crop field potentially suppresses the oscillations and brings forth stability in the system. Further, we observe that the system showcases the appearances of Generalized Hopf bifurcation, Zero-Hopf bifurcation, transcritical bifurcation and bistability. Overall, our findings manifest that by imparting knowledge among the farmers regarding the use of biopesticides and predators in the crop fields, the pest population can be effectively controlled.