Relevance of metric-free interactions in flocking phenomena

Topological analysis of complexity in multiagent systems

Social organisms at every level of evolutionary complexity live in groups, such as fish schools, locust swarms, and bird flocks. The complex exchange of multifaceted information across group members may result in a spectrum of salient spatiotemporal patterns characterizing collective behaviors. While instances of collective behavior in animal groups are readily identifiable by trained and untrained observers, a working definition to distinguish these patterns from raw data is not yet established. In this work, we define collective behavior as a manifestation of low-dimensional manifolds in the group motion and we quantify the complexity of such behaviors through the dimensionality of these structures. We demonstrate this definition using the ISOMAP algorithm, a data-driven machine learning algorithm for dimensionality reduction originally formulated in the context of image processing. We apply the ISOMAP algorithm to data from an interacting self-propelled particle model with additive noise, whose parameters are selected to exhibit different behavioral modalities, and from a video of a live fish school. Based on simulations of such model, we find that increasing noise in the system of particles corresponds to increasing the dimensionality of the structures underlying their motion. These low-dimensional structures are absent in simulations where particles do not interact. Applying the ISOMAP algorithm to fish school data, we identify similar low-dimensional structures, which may act as quantitative evidence for order inherent in collective behavior of animal groups. These results offer an unambiguous method for measuring order in data from large-scale biological systems and confirm the emergence of collective behavior in an applicable mathematical model, thus demonstrating that such models are capable of capturing phenomena observed in animal groups.

Collective motion of binary self-propelled particle mixtures

In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. More precisely, we consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant magnitude. Within each species, the particles try to achieve polar alignment of their velocity vectors, whereas we analyze the cases of preferred polar, antiparallel, as well as perpendicular alignment between particles of different species. Our focus is on the effect that the interplay between the two species has on the threshold densities for the onset of collective motion and on the nature of the solutions above onset. For this purpose, we start from suitable Langevin equations in the particle picture, from which we derive mean field equations of the Fokker-Planck type and finally macroscopic continuum field equations. We perform particle simulations of the Langevin equations and linear stability analyses of the Fokker-Planck and macroscopic continuum equations, and we numerically solve the Fokker-Planck equations. Both spatially homogeneous and inhomogeneous solutions are investigated, where the latter correspond to stripelike flocks of collectively moving particles. In general, the interaction between the two species reduces the threshold density for the onset of collective motion of each species. However, this interaction also reduces the spatial organization in the stripelike flocks. The case that shows the most interesting behavior is the one of preferred perpendicular alignment between different species. There a competition between polar and truly nematic orientational ordering of the velocity vectors takes place within each particle species. Finally, depending on the alignment rule for particles of different species and within certain ranges of particle densities, identical and inverted spatial density profiles can be found for the two particle species. The system under investigation is confined to two spatial dimensions.

Reciprocal relationships in collective flights of homing pigeons

Collective motion of bird flocks can be explained via the hypothesis of many wrongs and/or a structured leadership mechanism. In pigeons, previous studies have shown that there is a well-defined hierarchical structure and certain specific individuals occupy more dominant positions, suggesting that leadership by the few individuals drives the behavior of the collective. Conversely, by analyzing the same datasets, we uncover a more egalitarian mechanism. We show that both reciprocal relationships and a stratified hierarchical leadership are important and necessary in the collective movements of pigeon flocks. Rather than birds adopting either exclusive averaging or leadership strategies, our experimental results show that it is an integrated combination of both compromise and leadership which drives the group's movement decisions.

Inferring the rules of interaction of shoaling fish

Collective motion, where large numbers of individuals move synchronously together, is achieved when individuals adopt interaction rules that determine how they respond to their neighbors' movements and positions. These rules determine how group-living animals move, make decisions, and transmit information between individuals. Nonetheless, few studies have explicitly determined these interaction rules in moving groups, and very little is known about the interaction rules of fish. Here, we identify three key rules for the social interactions of mosquitofish (Gambusia holbrooki): (i) Attraction forces are important in maintaining group cohesion, while we find only weak evidence that fish align with their neighbor's orientation; (ii) repulsion is mediated principally by changes in speed; (iii) although the positions and directions of all shoal members are highly correlated, individuals only respond to their single nearest neighbor. The last two of these rules are different from the classical models of collective animal motion, raising new questions about how fish and other animals self-organize on the move.

Angle restriction enhances synchronization of self-propelled objects

Understanding the synchronization process of self-propelled objects is of great interest in science and technology. We propose a synchronization model for a self-propelled objects system in which we restrict the maximal angle change of each object to θ(R). At each time step, each object moves and changes its direction according to the average direction of all of its neighbors (including itself). If the angle change is greater than a cutoff angle θ(R), the change is replaced by θ(R). We find that (i) counterintuitively, the synchronization improves significantly when θ(R) decreases, (ii) there exists a critical restricted angle θ(Rc) at which the synchronization order parameter changes from a large value to a small value, and (iii) for each noise amplitude η, the synchronization as a function of θ(R) shows a maximum value, indicating the existence of an optimal θ(R) that yields the best synchronization for every η.