A Mathematical Modelling of a Plant-Herbivore Community with Additional Effects of Food on the Environment

Abstract

     By taking into account various food components in the ecosystem, the research intends to develop a set of difference equations to simulate a plant-herbivore interaction of Holling Type II. We determine the local stability of the equilibrium points for the scenarios of extinction, semi-extinction (extinction for one species), and coexistence using the Linearized Stability Theorem. For a suitable Lyapunov function, we investigate theoretical findings to determine the global stability of the coexisting equilibrium point. It is clear that the system exhibits both Flip and Neimark-Sacker bifurcation under particular circumstances using the central manifold theorem and the bifurcation theory. Numerical simulations are done by MATLAB which are used to validate our conclusions.