A Dimensional Reduction Analysis of the Self-propelled Particle Model

Abstract

Locusts continue to have devastating effects on the modern world. The swarming behavior of locusts emerges from the individual motion of each locust. How complex organized motion arises within animals represents a large area of research. The selfpropelled particle (SPP) model developed by Vicsek et al. (1995) successfully creates swarming behavior similar to that observed by locusts studied by Buhl et al. (2006). The SPP model creates a high dimensional data set of the positions and velocities of each locust at each time step. A better understanding of the dynamics of the SPP model could be used to control swarms of locusts before they destroy crops. Dimensional reduction techniques are used to discover if there exists an underlying substructure within the data. Both principal component analysis (PCA) and diffusion map analysis (DMA) identify the average velocity of the locusts, the alignment, as an important variable when tracking the switching behavior of particles on a one-dimensional domain. Further analysis identifies the relationship between the probability of switching and the alignment. The alignment of the swarm can be forced to switch by artificially changing the velocity of individual locusts to move against the swarm. The minimum number of locusts required to force a switch, known as the critical number, is found as a function of the alignment. When the alignment is near 0, setting 6 locusts out of 30 (20% of the population) is enough to result in a change in alignment 90% of the time. Future work could expand on these findings to see if they apply in vivo.