Related papers: Generalized solutions to bounded-confidence models
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
This paper proposes and analyzes a novel multi-agent opinion dynamics model in which agents have access to actions which are quantized version of the opinions of their neighbors. The model produces different behaviors observed in social…
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…
We consider a discrete set of individual agents interacting with a continuum. Examples might be a predator facing a huge group of preys, or a few shepherd dogs driving a herd of sheeps. Analytically, these situations can be described…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it's only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential…
An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is…
Distributed control increases system scalability, flexibility, and redundancy. Foundational to such decentralisation is consensus formation, by which decision-making and coordination are achieved. However, decentralised multi-agent systems…
It is studied the Cauchy problem for the equations of Burgers' type but with bounded dissipation flux. Such equations degenerate to hyperbolic ones as the velocity gradient tends to infinity. Thus the discontinuous solutions are permitted.…
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…
A general theory of innovation and progress in human society is outlined, based on the combat between two opposite forces (conservatism/inertia and speculative herding "bubble" behavior). We contend that human affairs are characterized by…
Structural Causal Models (SCMs) provide a popular causal modeling framework. In this work, we show that SCMs are not flexible enough to give a complete causal representation of dynamical systems at equilibrium. Instead, we propose a…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
Coordination games with explicit spatial or relational structure are of interest to economists, ecologists, sociologists, and others studying emergent global properties in collective behavior. When assemblies of individuals seek to…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
The Deffuant-Weisbuch (DW) model is a well-known bounded-confidence opinion dynamics that has attracted wide interest. Although the heterogeneous DW model has been studied by simulations over $20$ years, its convergence proof is open. Our…
The idea of a hierarchical spatial organization of society lies at the core of seminal theories in human geography that have strongly influenced our understanding of social organization. In the same line, the recent availability of…
Many empirical networks are intrinsically pluralistic, with interactions occurring within groups of arbitrary agents. Then the agent in the network can be influenced by types of neighbors, common examples include similarity, opposition, and…
Mean-field equations have been developed recently to approximate the dynamics of the Deffuant model of opinion formation. These equations can describe both fully-mixed populations and the case where individuals interact only along edges of…
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous…