Impact of delay parameter on plant-herbivore dynamics under allee effect

Abstract

Abstract In this paper, plant-herbivore dynamics have been studied under the Allee effect using delay differential equations. The state variables considered are: plant population and herbivores. The boundedness and positivity of solutions are established. The interior equilibrium point is calculated for both, strong and weak Allee effect. It is shown that both the populations-plant and herbivores perish under the strong Allee effect. The stability of the system around the interior equilibrium under weak Allee effect is checked. Hopf-Bifurcation occurred at the critical value of the delay parameter. Numerical results have been supported graphically using MATLAB.