Related papers: Differential Equations Modeling Crowd Interactions
Modeling realistic pedestrian trajectories requires accounting for both social interactions and environmental context, yet most existing approaches largely emphasize social dynamics. We propose \textbf{EnvSocial-Diff}: a diffusion-based…
In order to investigate collective effects of interactions between pedestrians and attractions, this study extends the social force model. Such interactions lead pedestrians to form stable clusters around attractions, or even to rush into…
A general procedure to formulate asexual (unstructured, deterministic) population dynamical models resulting from individual pairwise interactions is proposed. Individuals are characterized by a continuous strategy that represents all their…
Interacting individuals in complex systems often give rise to coherent motion exhibiting coordinated global structures. Such phenomena are ubiquitously observed in nature, from cell migration, bacterial swarms, animal and insect groups, and…
Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…
It is suggested that the motion of pedestrians can be described as if they would be subject to `social forces'. These `forces' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal…
We present a convergence result from nonlocal to local behavior for a system of nonlocal balance laws. The velocity field of the underlying conservation laws is diagonal. In contrast, the coupling to the remaining balance laws involves a…
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.…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…
The simulation of the dynamical behavior of pedestrians and crowds in spatial structures is a consolidated research and application context that still presents challenges for researchers in different fields and disciplines. Despite…
We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the…
Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena,…
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…
The simulation of pedestrian crowd that reflects reality is a major challenge for researches. Several crowd simulation models have been proposed such as cellular automata model, agent-based model, fluid dynamic model, etc. It is important…
It is very important to understand urban mobility patterns because most trips are concentrated in urban areas. In the paper, a new model is proposed to model collective human mobility in urban areas. The model can be applied to predict…
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…
We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…
Collective behavior is commonly attributed to direct interactions among system components. Using a minimal stochastic model, we show that higher-order collective structure can instead emerge from shared stochastic environments, even in the…
In this chapter, we discuss the mathematical modeling of egressing pedestrians in an unknown environment with multiple exits. We investigate different control problems to enhance the evacuation time of a crowd of agents, by few informed…