An "adaptive" approach to control explosive aphid populations
Classical models of aphid population dynamics are unable to explain multi-peak patterns in field populations. We consider the variable carrying capacity model (VCM), which can generate such complex multi-peak dynamics, but is also demonstrated to show finite-time blow-up behavior via a sign switching structural instability. We build an adaptive behavioral model with a density-dependent switch to stabilize growth, effectively eliminating blow-up, and also capable of generating multiple peaks. Furthermore, guided by empirical work on environment drivers for pests, we devise a non-autonomous model with time-dependent host plant fitness, successfully connecting transient population dynamics with abiotic drivers such as flooding. Finally, we discuss the practical significance of the results through the Economic Threshold (ET) and Economic Injury Level (EIL) calculation for all models. Our simulations all clearly show that aphid abundances exceed these threshold levels, and control is required. Our work provides a stable and biologically relevant prediction scheme for pest outbreaks and their management strategy.