Vegetation community plays a pivotal role in various geomorphic processes. The growth of vegetation intrinsically depends on the effective shear stresses exerted by the flow of material (e.g., water or soil) along the slope. We comparatively assess the growth and decay of vegetation using linear and logistic growth model coupled with a runoff erosion model. The linear growth model predicts a sharp decrease in the non-dimensional vegetation profile from the upper reach to the lower part along the slope. However, the logistic growth model delivers a smooth gradual decrease in the vegetation extent. Additionally, we propose a stochastic model to capture the role of internal and external factors in the dynamics of vegetation growth using two Gaussian noises. The steady probability distribution functions from the stochastic model provide insights about the role of different noises on the reaction of the system and suggest that bio-environmental factors are difficult to segregate from one another.

$\bf{Highlights}$

$\bullet$ Comparative study between logistic and linear vegetation growth model coupled with a surface erosion model.

$\bullet$ Steady-state equilibrium vegetation profile along any slope suggests that the logistic growth model is more realistic.

$\bullet$ Effect of Gaussian noises in vegetation growth has been demonstrated with the aid of stationary probability distribution.