Locust swarms are social aggregations consisting of large numbers of individuals (on the order of 10⁷-10⁹) that cohesively travel great distances over an extended period of time. Often observed in northern Africa, these swarms tend to follow a basic pattern; locusts at the front of the swarm land and rest on the ground until overtaken by the back of the swarm, at which point they take off and make their way to the front of the swarm. When viewed from the side it resembles a wheel rolling along [1-4].

Previous research attempts have been made using traveling bands along with density gradients [5]. Our model relies on the attraction-repulsion forces exerted on an individual by the others in the swarm. Basic assumptions included a strong desire to maintain group cohesion while short-range repulsion kept individuals from running into each other. To meet these requirements, we assume that the velocity is the sum of the contributions of all other locusts in the swarm; these contributions scale like a Morse potential [6]:

where x is the inner-locust distances.

In Figure 1 we see a swarm suspended in mid air. Upon examination of the F, L parameter space, we observed that a small portion of parameter space, namely where FL³ < 1, held the necessary condition that as N increased, the swarm density remained roughly constant. Figure 1 shows the lattice structure that is maintained when operating in this space.

Figure 2 is a swarm that has settled onto the ground after the addition of gravity. When taking values from the above mentioned section of parameter space, a small increase in spacing between the row of locusts on the ground and the row right above them is observed. This effect is more greatly noted when using values of F and L not from this space, as seen in Figure 3.

Figure 4 is a movie of a rolling swarm with values of F and L coming from the desired section. Unfortunately, these numbers do not lead to the desired behavior that is observed in real life. Many locusts are left behind and the swarm appears to be smearing out as opposed to rolling.

Figure 5 is another movie with values coming from outside of the calculated space. Here we see that the swarm rolls quite well and follows the general observed behavior. However, the part of the swarm in the air still remains circular, even with the addition of noise.

Overall, we were encouraged with the results of our study. We were able to achieve a rolling swarm, which was the ultimate goal. However, the swarm that rolls properly will become more dense as N increases. During further study, we plan to look at ways to have the swarm roll as it should, but also increase in size as N grows larger.