Catastrophic behavior of aphid population dynamics: An analysis of swallowtail model

Abstract

Catastrophe phenomena are frequent in insect ecology, especially in aphid populations. Complexity of this phenomenon urges different modeling frameworks other than traditional methodologies to understand the trajectories of their behavior. Situations like this can be best handled using catastrophe theory. A few numbers of experiments have been conducted to develop catastrophe models in insect ecology, especially for aphids, and most of them are based on cusp catastrophe theory which is a lower dimensional model. However few attempts using higher dimensional models such as swallowtail or butterfly theory to analyze aphid population dynamics are also exist. In this paper we tried to analyze a recently developed higher dimensional catastrophe theory model (APHIDSim) in order to identify catastrophe regions, and used independent data to identify if catastrophic behavior is observed in the data and consequently to further verify the model. Here we found that identifying catastrophe regions is possible using catastrophe theory model, and it can be used to analyze catastrophes in insect ecology by graphically interpreting the simulated results. Increasing of insect population is intrinsically catastrophic and catastrophes (jumps) occur between states even if the driving variables still change smoothly. The results further verified the previously developed model, and we suggest that insect management program developers should consider this phenomenon when they design the management strategies for insect controlling.

Keywords

• catastrophe theory
• cusp model
• swallowtail model
• aphid ecology
• population dynamics
• ecological software