Related papers: Self-organization on Riemannian manifolds
We investigate a model for collective behaviour with intrinsic interactions on smooth Riemannian manifolds. For regular interaction potentials, we establish the local well-posedness of measure-valued solutions defined via optimal mass…
We investigate a model for collective behaviour with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle…
We investigate the long-time behaviour of solutions to a nonlocal partial differential equation on smooth Riemannian manifolds of bounded sectional curvature. The equation models self-collective behaviour with intrinsic interactions that…
This paper investigates a system of nonlocal continuity equations modelling the interaction of two species coupled through Riesz-type potentials. The model incorporates self- and cross-interaction kernels of possibly different fractional…
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical points of the associated interaction energy) for interaction…
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighbourhood. In the first-order model the location of each…
After summarizing basic features of self-organization such as entropy export, feedbacks and nonlinear dynamics, we discuss several examples in biology. The main part of the paper is devoted to a model of active Brownian motion that allows a…
We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…
We investigate an aggregation model with intrinsic interactions on the special orthogonal group $SO(3)$. We consider a smooth interaction potential that depends on the squared intrinsic distance, and establish local and global existence of…
Recently solutions to the aggregation equation on compact Riemannian Manifolds have been studied with different techniques. This work demonstrates the small time existence of measure-valued solutions for suitably regular intrinsic…
The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual…
We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the…
Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational…
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…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions come from a uniformly closed algebra generated by functions…
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…