A Comparative Analysis of Diffusion Maps and the Coarse-Grained Alignment Dynamics of Self Propelled Particle Models

Abstract

An informed global response to the issue of locust swarming is tantamount to preserving agricultural investments and the quality of life in the developing world. The more that can be learned from the simulatable phenomenon of locust swarming, the better prepared the world will be to address the issue wherever it appears. Buhl et al. (2006) developed a Self Propelled Particle (SPP) Model for locust movement capable of simulating collected data on one dimensional locust movement, creating the foundation for Yates et al. (2007) and his work on using equation-free analysis methods to define the underlying pattern of general alignment in the SPP model using Stochastic Differential Equations (SDEs). Szeto (2009) then augmented the complexity of the SPP and SDE analysis by introducing a locust particle capable of leading the motion dynamics of the locust population in his work on the informed leader SPP model. Expanding on the previous analytical work done on these computational models of locust movement, applying nonlinear dimensionality reduction techniques to the raw data from the SPP model has produced high-priority variables correlated to the alignment variable previously studied in both the leader and non-leader models. Measuring and defining the relationship between the chosen method of nonlinear dimensionality reduction, diffusion mapping, has proven strong correlations between the produced variable and the aforementioned alignment variable. Equation-free analysis performed on the two significant variables has corroborated the evidence of the correlation. Additionally, further analysis of the influence the informed leader has on swarm motion dynamics has also proven consistent in both analytical variables. Further work should be done with more complex non-linear dimensionality reduction techniques to ascertain the most efficient way to process locust population motion data on a much larger scale.