Related papers: Generalized solutions to bounded-confidence models
We study the uniform boundedness of solutions to reaction-diffusion systems possessing a Lyapunov-like function and satisfying an {\it intermediate sum condition}. This significantly generalizes the mass dissipation condition in the…
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the…
Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a…
This paper deals with continuous-time opinion dynamics that feature the interplay of continuous opinions and discrete behaviours. In our model, the opinion of one individual is only influenced by the behaviours of fellow individuals. The…
With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…
We consider a fourth-order extension of the Allen-Cahn model with mixed-diffusion and Navier boundary conditions. Using variational and bifurcation methods, we prove results on existence, uniqueness, positivity, stability, a priori…
Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in…
The bounded confidence model represents a widely adopted framework for modeling opinion dynamics wherein actors have a continuous-valued opinion and interact and approach their positions in the opinion space only if their opinions are…
It is shown, that the Boltzmann-like equations allow the formulation of a very general model for behavioral changes. This model takes into account spontaneous (or externally induced) behavioral changes and behavioral changes by pair…
Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness theorem for systems of nonlocal conservation laws in several…
Large Language Models (LLMs) can be deployed in situations where they process positive/negative interactions with other agents. We study how this is done under the sociological framework of social balance, which explains the emergence of…
We study an opinion dynamics model in which agents reach compromise via pairwise interactions. When the opinions of two agents are sufficiently close, they both acquire the average of their initial opinions; otherwise, they do not interact.…
Non-Bayesian social learning theory provides a framework that models distributed inference for a group of agents interacting over a social network. In this framework, each agent iteratively forms and communicates beliefs about an unknown…
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the…
Multi-Context Systems are an expressive formalism to model (possibly) non-monotonic information exchange between heterogeneous knowledge bases. Such information exchange, however, often comes with unforseen side-effects leading to violation…
The question how social norms can emerge from microscopic interactions between individuals is a key problem in social sciences to explain collective behavior. In this paper we propose an agent-based model to show that randomly distributed…
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…
Models of opinion dynamics play a major role in various disciplines, including economics, political science, psychology, and social science, as they provide a framework for analysis and intervention. In spite of the numerous mathematical…