Related papers: Differential Equations Modeling Crowd Interactions
In a recent series of papers, we proposed a mathematical model for the dynamics of a group of interacting pedestrians. The model is based on a non-Newtonian potential, that accounts for the need of pedestrians to keep both their interacting…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We consider here a logistic equation, modeling processes of nonlocal character both in the diffusion and proliferation terms. More precisely, for populations that propagate according to a L\'evy process and can reach resources in a…
This paper presents a new approach to behavioral-social dynamics of pedestrian crowds by suitable development of methods of the kinetic theory. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well…
We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the…
Animals use various processes to inform themselves about their environment and make decisions about how to move and form their territory. In some cases, populations inform themselves of competing groups through observations at distances,…
In this paper we model pedestrian flows evacuating a narrow corridor through an exit by a one-dimensional hyperbolic conservation law with a non-local constraint. Existence and stability results for the Cauchy problem with Lipschitz…
We address the study of a class of 1D nonlocal conservation laws from a numerical point of view. First, we present an algorithm to numerically integrate them and prove its convergence. Then, we use this algorithm to investigate various…
We prove global existence, uniqueness and $\L1$ stability of solutions to general systems of nonlocal conservation laws modeling multiclass vehicular traffic. Each class follows its own speed law and has specific effects on the other…
Many organisms in nature use local interactions to generate global cooperative phenomena. To unravel how the behavior of individuals generates effective interactions within a group, we introduce a simple model, wherein each agent senses the…
A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead,…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
The evolutionary mechanisms of cooperative behavior represent a fundamental topic in complex systems and evolutionary dynamics. Real-world collective interactions, particularly in multi-agent systems, are often characterized by…
In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We are specifically concerned with a new agent-based, continuous-in-space,…
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…
We explore the emergence of nonequilibrium collective motion in disordered non-thermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
This is a brief "proof of concept" article that shows nonlocal diffusion is well suited to the study of pattern formation and the particular application of public sentiment. We use a nonlocal reaction-diffusion equation to model the…
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…