Butterfly catastrophe model for wheat aphid population dynamics: Construction, analysis and application

• A butterfly model for aphid population dynamics is proposed.
• The model is implemented by integrating four controlling factors.
• Growth of wheat aphid population is basically a catastrophic behavior.
• Sudden jumps occur from one state to another when control factors change smoothly.

In agriculture, a population catastrophic phenomenon exists in many species of insects such as wheat aphids. Numerous previous attempts have been made to describe this dynamic behavior of insect populations using mathematical models in order to develop efficient biological control measures. However, most of the models are limited to no more than three controlling variables and restricted in theoretical analysis, thus, are not enough to cope with complicated ecological systems. Catastrophe theory, one of the earliest dynamic theories, can be used to address this problem more comprehensively. In this study, we propose using butterfly catastrophe theory to build a wheat aphid population dynamics model as a function of four controlling factors (natural enemy, weather factor, pesticide effect and carrying capacity). We used data collected by Ecology and Integrated Pest Management Laboratory in Northwest A & F University to verify the model. Model development, parameter estimation and verification results are presented. The results indicate that the butterfly catastrophe model can be applied to analyze aphid population dynamics considering four controlling variables. Effective management strategies for preventing catastrophic increase of wheat aphids can be carried out by changing the four controlling variables.