MatlabSPP

Matlab example code for the Self Propelled Particle (SPP) Model

This is a portion of the work I did on my senior thesis, A Dimensional Reduction Analysis of the Self-Propelled Particle Model. Put simply, there are a number of particles or "locusts" on a 1-dimensional ring. At each time step, their motion is governed by one simple rule: update the velocity based on the average velocity of each particle within a certain interaction radius. Some noise is added as well. This results in complex behavior where the whole "swarm" will move clockwise, then switch to counterclockwise after some time, and so forth. My thesis analyzed that behavior, focusing on the points where switches in direction occurred. Mainly, can these seemingly random switches be predicted?

The second portion of my thesis (not posted here) used this information to see how the swarm could be "forced" to switch directions. By identifying switch points and adjusting the velocity of certain locusts, ways in which the alignment (average velocity) could be controlled were explored.

Here is what each file does in this selection of code:

Functions

• SPPModel2.m - Outputs the positions and velocities of an SPP simulation
• initializedSpp.m - Outputs the positions and velocities of an SPP simulation with given initial conditions
• switchFrequency.m - Outputs how many times a switch occurs if the simulation is rerun multiple times with a given initial state
• switchPoints.m - Identifies where the switch points occur
• switchChecker.m - Verifies if a switch has occurred

Executable Code

• plotPositionAlignment.m - Visualizes the results of SPPModel2.m
• plotSwitchesAndPercentages.m - Visualizes the results of switchFrequency.m

Outputs (examples from running plotSwitchesAndPercentages.m)

• positions.fig - A Matlab figure showing the positions of all the locusts
• positions.png - A png file of the above
• positionszoom.fig - A Matlab fig file of the positions of all locusts near a switch point, demonstrating a change in direction
• positionszoom.png - A png file of the above
• alignment.png - The average velocity of the locusts at each time step. The red line represents the alignment and the marked switch points.
• switchPercent.png - The percentage of trials that result in a switch for a given number of steps before each the three marked switch points.
• average.png - An average of the above graph

My senior thesis

• Lavrov_2015_SeniorThesis - My thesis, in which the above code played a critical role.