# Mathematical models of swarming and social aggregation

@inproceedings{EdelsteinKeshetMathematicalMO, title={Mathematical models of swarming and social aggregation}, author={Leah Edelstein-Keshet} }

I survey some of the problems (both mathematical and biological) connected with aggregation of social organisms and indicate some mathematical and modelling challenges. I describe recent work with collegues on swarming behaviour. Examples discussed include (1) a model for locust migration swarms, (2) the effect of non-local interactions on swarm shape and dynamics, and (3) an individualbased model for the spacing of neighbors in a group. I. Background and previous work Many chemical and…

## 49 Citations

Swarming dynamics of a model for biological groups in two dimensions

- Physics, Biology
- 2003

Numerical simulations of a class of continuum models for the motion of a two-dimensional biological group under the influence of nonlocal social interactions reveal rotating mill-like swarms with circular cores and spiral arms.

Self-organized pattern formation in a swarm system as a transient phenomenon of non-linear dynamics

- Engineering
- 2012

This article presents a microscopic model (agent positions, directions and interactions are explicitly modelled) of mobile agents (or self-propelled particles) that is inspired by the ‘complex…

A Lagrangian-based Swarming Behavior in the Absence of Obstacles

- Mathematics
- 2010

Lagrangian swarm models consider long-range attraction and short-range repulsion
between individuals, moving with the velocity of the swarm’s centroid, as a seed in the
formation of the swarm…

Heterophilious Dynamics Enhances Consensus

- Computer Science, MathematicsSIAM Rev.
- 2014

Of particular interest to us are cases in which the self-organized behavior tends to concentrate into one cluster, reflecting a consensus of opinions, flocking of birds, fish, or cells, rendezvous of mobile agents, and, in general, concentration of other traits intrinsic to the dynamics.

Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups

- Geology, Computer ScienceSIAM J. Appl. Math.
- 2004

A continuum model for the motion of biological organisms experiencing social interactions and study its pattern-forming behavior, which takes the form of a conservation law in two spatial dimensions.

Simulation of human migration based on swarm theory

- Computer Science2010 13th International Conference on Information Fusion
- 2010

In the present analysis, swarming techniques were found to reproduce quite well the group movement and behavior of individuals over predefined surface conditions, as determined by driving forces, social interactions and environmental conditions.

Collective Behaviors Through Social Interactions in Bird Flocks

- Computer ScienceIEEE Circuits and Systems Magazine
- 2019

This article aims at providing a discussion of various facets of this interdisciplinary field, including simulation models, mathematical methods and control theory, on several models of collective behaviors in bird flocks, a representative kind of MAS.

Macroscopic and microscopic self-organization by nonlocal anisotropic interactions

- Computer Science
- 2009

This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different selforganized patterns…

Locust Collective Motion and Its Modeling

- Biology, Computer SciencePLoS Comput. Biol.
- 2015

A wide range of recent modeling and simulation approaches are described, from discrete agent-based models of self-propelled particles to continuous models of integro-differential equations, aimed at describing and analyzing the fascinating phenomenon of locust collective motion.

Analyzing the Mathematical Models behind the Collective Intelligence of Bees

- 2015

For any system, a mathematical model is a generalization and representation of its features in a very precise manner. In this paper, we carried out a survey on mathematical models behind the bees.…

## References

SHOWING 1-10 OF 33 REFERENCES

Mutual interactions, potentials, and individual distance in a social aggregation

- Mathematics, MedicineJournal of mathematical biology
- 2003

It is shown quantitatively how repulsion must dominate attraction to avoid collapse of the group to a tight cluster and the existence of a well-spaced locally stable state, having a characteristic individual distance.

Dynamical aspects of animal grouping: swarms, schools, flocks, and herds.

- Biology, MedicineAdvances in biophysics
- 1986

An attempt is made to describe the motion of grouping individuals kinematically as distinct from simple diffusion or random walk, to model the grouping on the basis of dynamics of animal motion, and to interpret the grouping from the standpoint of advection-diffusion processes.

Translating stochastic density-dependent individual behavior with sensory constraints to an Eulerian model of animal swarming

- Mathematics, MedicineJournal of mathematical biology
- 1994

An Eulerian model of density-dependent swarming which is derived directly from a Lagrangian model in which individuals with limited sensing distances seek a target density of neighbors, and accurately predicts statistically stationary swarm characteristics, such as expected density distribution.

Do travelling band solutions describe cohesive swarms? An investigation for migratory locusts

- Computer Science
- 1998

Several hypotheses for the swarming behaviour in locusts are explored, with a goal of understanding how swarm cohesion can be maintained by the huge population of insects over long distances and long periods of time.

A non-local model for a swarm

- Mathematics
- 1999

Abstract. This paper describes continuum models for swarming behavior based on non-local interactions. The interactions are assumed to influence the velocity of the organisms. The model consists of…

MODELLING SOCIAL ANIMAL AGGREGATIONS

- Psychology
- 1994

It is hard to find animals in nature that do not aggregate for one reason or another. The details of such aggregations are important because they influence numerous fundamental processes like…

Self-organizing Dynamic Model of Fish Schooling

- Mathematics
- 1994

Abstract Fish schools show a high degree of polarization in the absence of a leader or external stimuli. In this paper the problems of the collective motion of fish schooling are analyzed, and the…

Geometry for the selfish herd.

- Mathematics, MedicineJournal of theoretical biology
- 1971

An antithesis to the view that gregarious behaviour is evolved through benefits to the population or species is presented, and simply defined models are used to show that even in non-gregarious species selection is likely to favour individuals who stay close to others.

Models of dispersal in biological systems

- Mathematics, MedicineJournal of mathematical biology
- 1988

Two stochastic processes that model the major modes of dispersal that are observed in nature are introduced, and explicit expressions for the mean squared displacement and other experimentally observable quantities are derived.

Animal group forces resulting from predator avoidance and competition minimization

- Biology, MedicineJournal of theoretical biology
- 1999

A new model to explain animal spacing, based on a trade-off between foraging efficiency and predation risk, is derived from biological principles. The model is able to explain not only the general…