相关论文: Nonlocal Crowd Dynamics Models for several Populat…

This paper mainly focuses on solving the dynamic optimization of the planar controlled crowd motion models with obstacles which is an application of a class of optimal control problems governed by a general perturbed nonconvex sweeping…

In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…

We study regularity of a hydrodynamic singular model of collective behavior introduced in \cite{ST1}. In this note we address the question of global well-posedness in multi-dimensional settings. It is shown that any initial data $(u,\rho)$…

The formation, movement and gluing of clusters can be described through a system of non local balance laws. Here, the well posedness of this system is obtained, as well as various stability estimates. Remarkably, qualitative properties of…

Dense pedestrian crowds may pose significant safety risks, yet their underlying dynamics remain insufficiently understood to reliably prevent accidents. In these environments, physical interactions and contact forces fundamentally shape the…

Crowd flow describes the elementary group behavior of crowds. Understanding the dynamics behind these movements can help to identify various abnormalities in crowds. However, developing a crowd model describing these flows is a challenging…

Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…

This paper addresses the theoretical foundations of pedestrian models for crowd dynamics. While the topic gains momentum, current models differ widely in their mathematical structure, even if we only consider continuous agent-based models.…

Understanding how people move in the urban area is important for solving urbanization issues, such as traffic management, urban planning, epidemic control, and communication network improvement. Leveraging recent availability of large…

By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…

The expansion of global electricity distribution systems necessitates the deployment of massive infrastructure. Assessing its implications from a spatial and material perspective requires an understanding of the core drivers of a…

We investigate a class of nonlocal conservation laws in several space dimensions, where the continuum average of weighted nonlocal interactions are considered over a finite horizon. We establish well-posedness for a broad class of flux…

Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…

A multi-agent model for individuals endowed with strategies and subject to diffusive effects is proposed. The microscopic state of each agent is described by a spatial position and a probability measure, interpreted as a mixed strategy,…

Population games can be regarded as a tool to study the strategic interaction of a population of players. Although several attention has been given to such field, most of the available works have focused only on the unconstrained case. That…

In this survey we consider mathematical models and methods recently developed to control crowd dynamics, with particular emphasis on egressing pedestrians. We focus on two control strategies: The first one consists in using special agents,…

For a large family of nonautonomous scalar-delayed differential equations used in population dynamics, some criteria for permanence are given, as well as explicit upper and lower bounds for the asymptotic behavior of solutions. The method…

Since the appearance of the classical paper of Lifshitz almost half a century ago, linear stability analysis of cosmological models is textbook knowledge. Until recently, however, little was known about the behavior of higher than linear…

We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…

The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…