Exploring a Simple Stochastic Mathematical Model Including Fear with a Linear Functional Response

This paper concentrates on a simple population model incorporating fear. Firstly, positivity and steady state analysis are performed, where the theoretical investigations show that change in level of fear prey does not effect local stability system around each equilibria (either stable or unstable). For deterministic model, numerical simulations plotted for density species as function various parameters. The coexisting shows only transcritical bifurcation, states intersect, is observed. Secondly, analysed with Gaussian noise term incorporated prey’s death rate. comprising turns into stochastic differential equations irregular related oscillations observed densities both species.