Effect of randomly fluctuating environment on autotroph-herbivore model system (Q1777886)

The authors consider a noninteractive type of autotroph-herbivore model system in which the removal rate of autotroph biomass has been taken as a Holling type -III function and they derive a local asymptotic stability condition and the existence of small amplitude periodic solution within a deterministic environment. The deterministic model is randomized by introducing additive Gaussian white noise leading to a system of Itô type of stochastic differential equation. Stochastic stability criteria of the model system under the influence of random environmental fluctuation are obtained through the convergence conditions of second-order moments.