Inferring causal relationship in coordinated flight of pigeon flocks

Dynamic Leadership Mechanism in Homing Pigeon Flocks

In recent years, an increasing number of studies have focused on exploring the principles and mechanisms underlying the emergence of collective intelligence in biological populations, aiming to provide insights for human society and the engineering field. Pigeon flock behavior garners significant attention as a subject of study. Collective homing flight is a commonly observed behavioral pattern in pigeon flocks. The study analyzes GPS data during the homing process and utilizes acceleration information, which better reflects the flock's movement tendencies during turns, to describe the leadership relationships within the group. By examining the evolution of acceleration during turning, the study unveils a dynamic leadership mechanism before and after turns, employing a more intricate dynamic model to depict the flock's motion. Specifically, during stable flight, pigeon flocks tend to rely on fixed leaders to guide homing flight, whereas during turns, individuals positioned in the direction of the flock's turn experience a notable increase in their leadership status. These findings suggest the existence of a dynamic leadership mechanism within pigeon flocks, enabling adaptability and stability under diverse flight conditions. From an engineering perspective, this leadership mechanism may offer novel insights for coordinating industrial multi-robot systems and controlling drone formations.

The structure inference of flocking systems based on the trajectories

The interaction between the swarm individuals affects the dynamic behavior of the swarm, but it is difficult to obtain directly from outside observation. Therefore, the problem we focus on is inferring the structure of the interactions in the swarm from the individual behavior trajectories. Similar inference problems that existed in network science are named network reconstruction or network inference. It is a fundamental problem pervading research on complex systems. In this paper, a new method, called Motion Trajectory Similarity, is developed for inferring direct interactions from the motion state of individuals in the swarm. It constructs correlations by combining the similarity of the motion trajectories of each cross section of the time series, in which individuals with highly similar motion states are more likely to interact with each other. Experiments on the flocking systems demonstrate that our method can produce a reliable interaction inference and outperform traditional network inference methods. It can withstand a high level of noise and time delay introduced into flocking models, as well as parameter variation in the flocking system, to achieve robust reconstruction. The proposed method provides a new perspective for inferring the interaction structure of a swarm, which helps us to explore the mechanisms of collective movement in swarms and paves the way for developing the flocking models that can be quantified and predicted.

Ordering kinetics in the active model B

We undertake a detailed numerical study of the Active Model B proposed by Wittkowski et al., [Nature Commun. 5, 4351 (2014)]2041-172310.1038/ncomms5351. We find that the introduction of activity has a drastic effect on the ordering kinetics. First, the domain growth law shows a crossover from the usual Lifshitz-Slyozov growth law for phase separation (L∼t^{1/3}, where t is the time) to a novel growth law (L∼t^{1/4}) at late times. Second, the equal-time correlation function of the density field exhibits dynamical scaling for a given activity strength λ, but the scaling function depends on λ.

Transfer entropy dependent on distance among agents in quantifying leader-follower relationships

Synchronized movement of (both unicellular and multicellular) systems can be observed almost everywhere. Understanding of how organisms are regulated to synchronized behavior is one of the challenging issues in the field of collective motion. It is hypothesized that one or a few agents in a group regulate(s) the dynamics of the whole collective, known as leader(s). The identification of the leader (influential) agent(s) is very crucial. This article reviews different mathematical models that represent different types of leadership. We focus on the improvement of the leader-follower classification problem. It was found using a simulation model that the use of interaction domain information significantly improves the leader-follower classification ability using both linear schemes and information-theoretic schemes for quantifying influence. This article also reviews different schemes that can be used to identify the interaction domain using the motion data of agents.

Maximum Markovian order detection for collective behavior

Many advances have been achieved in the study of collective behavior of animal groups and human beings. Markovian order is a significant property in collective behavior, which reveals the inter-agent interaction strategy of the system. In this study, we propose a method using the time-series data of collective behavior to determine the optimal maximum Markov order of time-series motion data so as to reflect the maximum memory capacity of the interacting network. Our method combines a time-delayed causal inference algorithm and a multi-order graphical model. We apply the method to the data of pigeon flocks, dogs, and a group of midges to determine their optimal maximum order for validation and construct high-order De Bruijn graphs as a stochastic model to describe their interacting relationships. Most temporal network data of animal movements can be effectively analyzed by our method, which may provide a practical and promising solution to detection of the optimal maximum Markovian order of collective behavior.

Speed inhomogeneity accelerates information transfer in polar flock

A collection of self-propelled particles (SPPs) shows coherent motion and exhibits a true long-range-ordered state in two dimensions. Various studies show that the presence of spatial inhomogeneities can destroy the usual long-range ordering in the system. However, the effects of inhomogeneity due to the intrinsic properties of the particles are barely addressed. In this paper we consider a collection of polar SPPs moving at inhomogeneous speed (IS) on a two-dimensional substrate, which can arise due to varying physical strengths of the individual particles. To our surprise, the IS not only preserves the usual long-range ordering present in homogeneous speed models but also induces faster ordering in the system. Furthermore, the response of the flock to an external perturbation is also faster, compared to the Vicsek-like model systems, due to the frequent update of neighbors of each SPP in the presence of the IS. Therefore, our study shows that an IS can promote information transfer in a moving flock.