The role of neighbours selection on cohesion and order of swarms

Abstract

We introduce a multi-agent model for exploring how selection of neighbours determines some aspects of order and cohesion in swarms. The model algorithm states that every agents' motion seeks for an optimal distance from the nearest topological neighbour encompassed in a limited attention field. Despite the great simplicity of the implementation, varying the amplitude of the attention landscape, swarms pass from cohesive and regular structures towards fragmented and irregular configurations. Interestingly, this movement rule is an ideal candidate for implementing the selfish herd hypothesis which explains aggregation of alarmed group of social animals.

Figure 1. An example of an agent's movement.

Individual 1, moves with speed towards individual 2 which is the nearest neighbour encompassed by the attention field, the blue region characterised by the angle . The stress zone of individual 2 is the red disk of radius .

Figure 2. The convergence time as a function of the speed , for different populations (, ).

Data points represent averages taken over different simulations, where the individual initial distribution is different. In the inset: as a function of . The continuous line is the fitted relation: .

Figure 3. Time evolution of the order parameters and averaged over 100 simulations.

The dashed line is the convergence probability of the ensemble of simulations. , , , and .

Figure 4. Examples of some characteristic configurations of the quasi-stationary states for different values (, and ).

The red dots represent the agents' position and the lines depict the Voronoi tessellation.

Figure 5. Order parameters and for different .

Data are averaged over 100 simulations when the system reaches the quasi-stationary state (, , and ).

Figure 6. The standard deviations of and for different .

Data are averaged over 100 simulations when the system reaches the quasi-stationary state (, , and ).

Figure 7. and as a function of the noise strength after iterations.

Data are averaged over 100 simulations (, , and ).

Figure 8. An active configuration obtained using the parameter , , , , , and .

After a rapid transient, during which the group density increases, we obtain a configuration qualitatively similar to the field observations of reference .

Figure 9. Time evolution of the sum of the areas of the Voronoi polygons (), normalised for its value at .

A significant reduction of the domain of danger is obtained after a few iterations of the algorithm.