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Related papers: A primer of swarm equilibria

200 papers

Despite their wide presence in various models in the study of collective behaviors, explicit swarming patterns are difficult to obtain. In this paper, special stationary solutions of the aggregation equation with power-law kernels are…

Analysis of PDEs · Mathematics 2016-02-23 José A. Carrillo , Yanghong Huang

Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…

Analysis of PDEs · Mathematics 2018-03-12 José A. Carrillo , Aneta Wróblewska-Kamińska , Ewelina Zatorska

We consider the problem of understanding the coordinated movements of biological or artificial swarms. In this regard, we propose a learning scheme to estimate the coordination laws of the interacting agents from observations of the swarm's…

Systems and Control · Electrical Eng. & Systems 2025-09-26 Christos Mavridis , Amoolya Tirumalai , John Baras

We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case,…

Analysis of PDEs · Mathematics 2019-12-03 Mihaï Bostan , José Antonio Carrillo

We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…

Dynamical Systems · Mathematics 2024-05-08 Blake McGrane-Corrigan , Oliver Mason , Rafael de Andrade Moral

In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown,…

Analysis of PDEs · Mathematics 2012-03-06 Andrea Tosin , Paolo Frasca

We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…

Probability · Mathematics 2025-10-21 Razvan C. Fetecau , Hui Huang , Jinniao Qiu

Morphological computing, the use of the physical design of a robot to ease the realization of a given task has been proven to be a relevant concept in the context of swarm robotics. Here we demonstrate both experimentally and numerically,…

Soft Condensed Matter · Physics 2026-01-13 Jeremy Fersula , Nicolas Bredeche , Olivier Dauchot

Collective behaviour in biological systems pitches us against theoretical challenges way beyond the borders of ordinary statistical physics. The lack of concepts like scaling and renormalization is particularly grievous, as it forces us to…

Statistical Mechanics · Physics 2017-10-11 A. Cavagna , D. Conti , C. Creato , L. Del Castello , I. Giardina , T. S. Grigera , S. Melillo , L. Parisi , M. Viale

Swarming behavior, where coherent motion emerges from the interactions of many mobile agents, is ubiquitous in physics and biology. Moreover, there are many efforts to replicate swarming dynamics in mobile robotic systems which take…

Adaptation and Self-Organizing Systems · Physics 2021-06-04 Ira B. Schwartz , Victoria Edwards , Jason Hindes

Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…

Populations and Evolution · Quantitative Biology 2025-04-16 Jonathan R. Potts

The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…

Statistical Mechanics · Physics 2015-01-12 Illes J. Farkas , Jeromos Kun , Yi Jin , Gaoqi He , Mingliang Xu

We consider an aggregation model with nonlinear diffusion in domains with boundaries and investigate the zero diffusion limit of its solutions. We establish the convergence of weak solutions for fixed times, as well as the convergence of…

Analysis of PDEs · Mathematics 2018-09-05 Razvan C. Fetecau , Mitchell Kovacic , Ihsan Topaloglu

In this article, we consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources…

Analysis of PDEs · Mathematics 2019-07-30 Idriss Mazari , Grégoire Nadin , Yannick Privat

We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…

Probability · Mathematics 2021-09-14 Aurélien Velleret

In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…

Dynamical Systems · Mathematics 2014-03-31 J. A. Carrillo , Y. Huang , S. Martin

We overview recent developments in the study of alignment hydrodynamics, driven by a general class of symmetric communication kernels. A main question of interest is to characterize the emergent behavior of such systems, which we quantify…

Analysis of PDEs · Mathematics 2021-02-19 Eitan Tadmor

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset $\Omega$ of Euclidean space. The approximation is good when a large number of…

Dynamical Systems · Mathematics 2025-12-09 A. D. Barbour , R. McVinish , P. K. Pollett

This work addresses the optimal birth control problem for invasive species in a spatial environment. We apply the method of semigroups to qualitatively analyze a size-structured population model in which individuals occupy a position in a…

Optimization and Control · Mathematics 2021-04-12 Manoj Kumar , Syed Abbas

We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader…

Computer Science and Game Theory · Computer Science 2026-03-26 Sam Ganzfried