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This paper focuses on a model for opinion dynamics, where the influence weights of agents evolve in time. We formulate a control problem of consensus type, in which the objective is to drive all agents to a final target point under suitable control constraints. Controllability is discussed for the corresponding problem with and without constraints on the total mass of the system, and control strategies are designed with the steepest descent approach. The mean-field limit is described both for the opinion dynamics and the control problem. Numerical simulations illustrate the control strategies for the finite-dimensional system.
In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a transport eq
In this paper, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions evolution. We explore the natural question of the large population limit with two approaches:
This paper is concerned with system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback controller wi
Motivated by its application in ecology, we consider an extended Klausmeier model, a singularly perturbed reaction-advection-diffusion equation with spatially varying coefficients. We rigorously establish existence of stationary pulse solutions by bl
We investigate the validity of a soliton dynamics behavior in the semi-relativistic limit for the nonlinear Schrodinger equation in $R^{N}, Nge 3$, in presence of a singular external potential.