Catastrophe control of aphid populations based on washout filter

Aphid populations cause stunted plant growth by extracting sap and can also induce cascading damage through the transmission of viruses. Because of their rapid reproduction, aphid populations can easily develop into large-scale outbreaks. Therefore, the effective management of aphid populations is of particular importance. In this paper, a catastrophe model is first proposed based on ecological principles, and its dynamical behaviour is analyzed by the qualitative theory of differential equations. Then, by considering the effects of natural enemy populations on the aphid population, a management model incorporating a washout filter is developed. Based on catastrophe control theory, the corresponding controllers are designed either to delay aphid outbreaks until the end of grain filling stage, or to stabilize the aphid population at the refuge level. Finally, computer simulations are carried out to verify the correctness of the results. The main contribution of this paper is the introduction of the washout filter to characterize the influence of natural enemy populations on aphid populations, which not only expands the application of catastrophe control theory, but also provides a new perspective for the management of aphid populations.