Related papers: Flocking of the Cucker-Smale and Motsch-Tadmor mod…
We present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered - including examples for the widely observed behavior of hierarchically interacting…
Diffusion processes have been applied with great success to model the dynamics of large populations throughout science, in particular biology. One advantage is that they bridge two different scales: the microscopic and the macroscopic one.…
Sampling from the $q$-state ferromagnetic Potts model is a fundamental question in statistical physics, probability theory, and theoretical computer science. On general graphs, this problem may be computationally hard, and this hardness…
Natural flocks (aligned) and swarms (non-aligned) both exhibit features of near-criticality, challenging their treatment as two ends of the same phase transition. We present a model for the aggregation of active individuals, in which their…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We study the multi-scale description of large-time collective behavior of agents driven by alignment. The resulting multi-flock dynamics arises naturally with realistic initial configurations consisting of multiple spatial scaling, which in…
We introduce a class of one-dimensional linear kinetic equations of Boltzmann and Fokker--Planck type, describing the dynamics of individuals of a multi-agent society questing for high status in the social hierarchy. At the Boltzmann level,…
We introduce a new class of models for emergent dynamics. It is based on a new communication protocol which incorporates two main features: short-range kernels which restrict the communication to local geometric balls, and anisotropic…
Social reinforcement and modular structure are two salient features observed in the spreading of behavior through social contacts. In order to investigate the interplay between these two features, we study the generalized epidemic process…
We present the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface, and many of its predictions for experiment. We find that such systems are stable, and have long-range orientational order, over a…
Background: The accumulation of deleterious mutations of a population directly contributes to the fate as to how long the population would exist. Muller's ratchet provides a quantitative framework to study the effect of accumulation.…
We have proposed a model based upon flocking on a complex network, and then developed two clustering algorithms on the basis of it. In the algorithms, firstly a \textit{k}-nearest neighbor (knn) graph as a weighted and directed graph is…
We study a class of individual-based, fixed-population size epidemic models under general assumptions, e.g., heterogeneous contact rates encapsulating changes in behavior and/or enforcement of control measures. We show that the…
In this work we focus on a natural class of population protocols whose dynamics are modelled by the discrete version of Lotka-Volterra equations. In such protocols, when an agent $a$ of type (species) $i$ interacts with an agent $b$ of type…
Collective motion - or flocking - is an emergent phenomena that underlies many biological processes of relevance, from cellular migrations to animal groups movement. In this work, we derive scaling relations for the fluctuations of the mean…
The purpose of this paper is to consider flocking formations of a second order dynamic system on a sphere with a Cucker-Smale type flocking operator and cooperative control. The flocking operator consists of a weighted control parameter and…
Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors,…
A wide variety of real-life networks share two remarkable generic topological properties: scale-free behavior and modular organization, and it is natural and important to study how these two features affect the dynamical processes taking…
We study the emergent dynamics of the relativistic kinetic Cucker-Smale (RKCS) model without assuming compactness in spatial and velocity support. In this setting, the lower bound of the kernel function in the nonlocal velocity alignment…
Consider the following asynchronous, opportunistic communication model over a graph $G$: in each round, one edge is activated uniformly and independently at random and (only) its two endpoints can exchange messages and perform local…