Related papers: Spatial flocking: Control by speed, distance, nois…
Understanding the population dynamics of ecological systems is crucial for predicting shifts in biodiversity and ensuring the protection of these systems. Established models often focus on pairwise species interactions, yet recent studies…
We propose a comprehensive dynamical model for cooperative motion of self-propelled particles, e.g., flocking, by combining well-known elements such as velocity-alignment interactions, spatial interactions, and angular noise into a unified…
Recent empirical observations of three-dimensional bird flocks and human crowds have challenged the long-prevailing assumption that a metric interaction distance rules swarming behaviors. In some cases, individual agents are found to be…
A standard belief on emerging collective behavior is that it emerges from simple individual rules. Most of the mathematical research on such collective behavior starts from imperative individual rules, like always go to the center. But how…
We consider a population of mobile agents able to make noisy observation of the environment and communicate their observation by production and comprehension of signals. Individuals try to align their movement direction with their…
Flocks of birds and schools of fish are familiar examples of spatial patterns formed by living organisms. In contrast to the patterns on the skins of, say, zebra and giraffe, the patterns of our interest are {\it transient} although…
We show that sensorial delay alters the collective motion of self-propelling agents with aligning interactions: In a two-dimensional Vicsek model, short delays enhance the emergence of clusters and swarms, while long or negative delays…
In collective motion, perceptually-limited individuals move in an ordered manner, without centralized control. The perception of each individual is highly localized, as is its ability to interact with others. While natural collective motion…
Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real…
Group behavior has received much attention as a test case of self-organization. There has been much written in recent years to investigate interactions within groups of agents. These agents can be animals moving in an interactive way, such…
Models of ordering dynamics allow to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to…
Many biological systems synchronize their movement through physical interactions. By far the most well studied examples concern physical interactions through a fluid: beating cilia, swimming sperm and worms, and flapping wings, all display…
We consider the Czir\'ok model for collective motion of locusts along a one-dimensional torus. In the model, each agent's velocity locally interacts with other agents' velocities in the system, and there is also exogenous randomness to each…
Collective behaviors such as swarming and flocking emerge from simple, decentralized interactions in biological systems. Existing models, such as Vicsek and Cucker-Smale, lack collision avoidance, whereas the Olfati-Saber model imposes…
The aim of the present paper is to elucidate the transition from collective to random behavior exhibited by various mathematical models of bird flocking. In particular, we compare Vicsek's model [Viscek et al., Phys. Rev. Lett. 75, 1226 --…
Empirical observations in marine ecosystems have suggested a balance of biological and advection time scales as a possible explanation of species coexistence. To characterise this scenario, we measure the time to fixation in neutrally…
Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy…
Swarms of large numbers of agents appear in many biological and engineering fields. Dynamic bi-stability of co-existing spatio-temporal patterns has been observed in many models of large population swarms. However, many reduced models for…
This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates''), followed…
Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where…