Dynamic Analysis of a Discrete-Time Plant Quality and Larch Budmoth Interaction Model Under Random Perturbations

Abstract

In ecosystems, almost all organisms suffer from external influences, which are assumed to be random perturbations. The aim of this paper is to investigate the effects of random perturbations on interacting populations. To solve this problem, we propose a discrete-time plant quality and larch budmoth interaction model with biological control. First of all, the model is theoretically analyzed, and the dynamic behavior of the population is qualitatively analyzed by numerical simulation. In addition, random perturbations are added to the model to observe the effects of random perturbations on the dynamic behavior of the budmoth population. The main results show that a random perturbation changes the number of blurred orbits of the system compared to the single population model with the same perturbation. Undeniably, it enhances the stability of the system. The model results, after adding random perturbations, are closer to reality, and in practice, we can also use random perturbations for resource management and pest control.