APHIDSim: A population dynamics model for wheat aphids based on swallowtail catastrophe theory

Controlling aphids is vital since they are serious pests of wheat as well as many agricultural crops in the world. To avoid adverse effects of total reliance on chemical insecticides so as to ensure the ecological well balance of the agricultural ecosystems, there is a need to have eco-friendly control measures like biological control. For this, a good understanding of their population dynamics is critically important. Though there are several criticisms, a number of experiments have been conducted to develop forecasting models or expert systems for identifying the population, rates of growth or the damage. Those models are based on a number of mathematical models, including catastrophe theory, especially the cusp model. However, many of them are limited to the theoretical models but not to the practical systems or software. This study is aimed to analyze population dynamics of wheat aphids and to build a computer program (APHIDSim) integrating the swallowtail catastrophe theory. We built a swallowtail model from the aphid population as a function of three controlling factors: weather, crop and natural enemy in order to analyze the swallowtail behavior of population dynamics of wheat aphids. The APHIDSim is implemented integrating the swallowtail model and analyzed aphid population data for swallowtail behavior. The results show that the increase of wheat aphid population (population dynamics) is essentially a catastrophic behavior and sudden jumps may occur from one state to another even though the control factors change smoothly.