Related papers: Asymptotically stable polarization of multi-agent …
Certain consensus seeking multi-agent systems can be formulated as gradient descent flows of a disagreement function. We study how known pathologies of gradient descent flows in Euclidean spaces carry over to consensus seeking systems that…
The aim of this article is to investigate the convergence properties of a heterogeneous consensus model on Stiefel manifolds. We consider each agent, without interaction, moving according to the flow determined by the fundamental vector…
Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…
Motivated by empirical research on bias and opinion formation, we formulate a multidimensional nonlinear opinion-dynamical model where agents have individual biases, which are fixed, as well as opinions, which evolve. The dimensions…
It is known that individual opinions on different policy issues often align to a dominant ideological dimension (e.g. "left" vs. "right") and become increasingly polarized. We provide an agent-based model that reproduces these two stylized…
A group behavior of a heterogeneous multi-agent system is studied which obeys an "average of individual vector fields" under strong couplings among the agents. Under stability of the averaged dynamics (not asking stability of individual…
Polarization and unexpected correlations between opinions on diverse topics (including in politics, culture and consumer choices) are an object of sustained attention. However, numerous theoretical models do not seem to convincingly explain…
This paper studies consensus problems for multi-agent systems defined on directed graphs where the consensus dynamics involves nonlinear and discontinuous functions. Sufficient conditions, involving the nonlinear functions and the topology…
A set of many identical interacting agents obeying a global additive constraint is considered. Under the hypothesis of equiprobability in the high-dimensional volume delimited in phase space by the constraint, the statistical behavior of a…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
We describe a model for polarization in multi-agent systems based on Esteban and Ray's classic measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on the beliefs of others and an underlying…
In this paper, the behavior of scalar multi-agent systems over networks subject to time-driven jumps. Assuming that all agents communicate through distinct communication digraphs at jump and flow times, the asymptotic multi-consensus…
Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this…
This paper addresses the bipartite consensus-control problem in open multi-agent systems containing both cooperative and antagonistic interactions. In these systems, new agents can join and new interactions can be formed over time.…
Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while sometimes chaotic,…
Stability and analysis of multi-agent network systems with state-dependent switching typologies have been a fundamental and longstanding challenge in control, social sciences, and many other related fields. These already complex systems…
In this paper, from the structural perspective, we propose a new stability analysis approach for the consensus of linear multi-agent systems. Different from the general tools: the Laplacian matrix based method and the Lyapunov's method,…
Polarization, defined as the emergence of sharply divided groups with opposing and often extreme views, is an increasingly prominent feature of modern societies. While many studies analyze this phenomenon in the context of single issues,…
Political polarization is perceived as a threat to democracies. Using the Galam model of opinion dynamics deployed in a five-dimensional parameter space, I show that polarization is the byproduct of an essential hallmark of a vibrant…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…