Dispersal effects on a discrete two-patch model for plant-insect interactions

A two-patch discrete time plant-insect model coupled through insect dispersal is studied. The model is based on three different phases: Plant growth is followed by the dispersal of insects followed by insect attacks. Our objective is to understand how different intensities of dispersal impact both local and global population dynamics of the two-patch model. Special attention is paid to two situations: When the single-patch model (i.e., in the absence of dispersal) is permanent and when the single-patch model exhibits Allee-like effects. The existence and stability of synchronous and asynchronous dynamics between two patches is explored. If the single-patch system is permanent, the permanence of the system in two patches is destroyed by extremely large dispersals and large attacking rates of insects, thus creating multiple attractors. If the single-patch model exhibits Allee-like effects, analytical and numerical results indicate that small intensity of dispersals can generate source-sink dynamics between two patches, while intermediate intensity of dispersals promote the extinction of insects in both patches for certain parameter ranges. Our study suggests a possible biology control strategy to stop the invasion of a pest by controlling its migration between patches.