A model for rolling swarms of locusts

By Chad M. Topaz, A. Bernoff, S. Logan, Wyatt Toolson. 2007

156 citations recorded by the source corpus.

Abstract.We construct an individual-based kinematic model of rolling migratory locust swarms. The model incorporates social interactions, gravity, wind, and the effect of the impenetrable boundary formed by the ground. We study the model using numerical simulations and tools from statistical mechanics, namely the notion of H-stability. For a free-space swarm (no wind and gravity), as the number of locusts increases, the group approaches a crystalline lattice of fixed density if it is H-stable, and in contrast becomes ever denser if it is catastrophic. Numerical simulations suggest that whether or not a swarm rolls depends on the statistical mechanical properties of the corresponding free-space swarm. For a swarm that is H-stable in free space, gravity causes the group to land and form a crystalline lattice. Wind, in turn, smears the swarm out along the ground until all individuals are stationary. In contrast, for a swarm that is catastrophic in free space, gravity causes the group to land and form a bubble-like shape. In the presence of wind, the swarm migrates with a rolling motion similar to natural locust swarms. The rolling structure is similar to that observed by biologists, and includes a takeoff zone, a landing zone, and a stationary zone where grounded locusts can rest and feed.

Subfields: Global and Planetary Change, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/d16c65cdf9b0964bd901d8929fec4c5769895258

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Citations in the corpus

Grasshopper Optimisation Algorithm: Theory and application (2017, methodology): “The mathematical model employed to simulate the swarming behaviour of grasshoppers is presented as follows [39]: where 𝑋 𝑖 defines the position of the i-th grasshopper, 𝑆 𝑖 is the social interaction, 𝐺 𝑖 is the gravity force on the i-th grasshopper, and 𝐴 𝑖 shows the wind advection.”
Grasshopper optimization algorithm for multi-objective optimization problems (2017, methodology): “The mathematical equations and formulas proposed for this algorithm are given as follows [40, 41].”
Ring patterns and their bifurcations in a nonlocal model of biological swarms (2015, background): “Introduction Mathematical models for swarming, schooling, and other aggregative behavior in biology have given us many tools to understand the fundamental behavior of collective motion and pattern formation that occurs in nature [10, 6, 2, 26, 25, 14, 7, 13, 27, 19, 33, 32, 23, 11, 17, 37, 38, 34, 3”
Dimensionality of Local Minimizers of the Interaction Energy (2012, background): “Analogously in applications to biological sciences [27, 26, 33, 4, 14], individuals in a social aggregate (e.”