Stability of a budworm growth model with random perturbations

A budworm growth model perturbed by both white noises and regime switchings is proposed and analyzed. It is proven that there is a threshold. If this threshold is positive, then the model has a unique ergodic stationary distribution; if this threshold is negative, then the zero solution of the model is stable. The results show that both white noises and regime switchings can change the stability of the model greatly. Several numerical simulations based on realistic data are also introduced to illustrate the main results.