Related papers: Complexity Reduction Ansatz for Systems of Interac…
The Kuramoto model, describing the synchronization dynamics of coupled oscillators, has been generalized in many ways over the past years. One recent extension of the model replaces the oscillators, originally characterized by a single…
This note concerns the evolution of multi-agent systems on networks over Riemannian manifolds. The motion of each agent is governed by the gradient descent flow of a disagreement function that is a sum of (squared) distances between pairs…
Motivated by a geometric decomposition of the vector field associated with the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation for finite-level open quantum systems, we propose a generalization of the recently introduced contact…
In this paper we investigate the possibility of reducing the complexity of a system composed of a large number of interacting agents, whose dynamics feature a symmetry breaking. We consider first order stochastic differential equations…
We study synchronization of Kuramoto oscillators in strongly modular networks in which the structure of the network inside each community is averaged. We find that the dynamics of the interacting communities can be described as an ensemble…
A bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces. It is shown that there exists a finite-dimensional center manifold on a space of generalized functions. The…
We apply path-integral techniques to study the dynamics of agent-based models with asymmetric information structures. In particular, we devise a batch version of a model proposed originally by Berg et al. [Quant. Fin. 1 (2001) 203], and…
Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs…
The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N…
Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. Thus…
The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The…
The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson…
It is shown that applying manifold learning techniques to Poincar\'e sections of high-dimensional, chaotic dynamical systems can uncover their low-dimensional topological organization. Manifold learning provides a low-dimensional embedding…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
The dynamics of patterns in large two-dimensional domains remains a challenge in non-equilibrium phenomena. Often it is addressed through mild extensions of one-dimensional equations. We show that full 2D generalizations of the latter can…
The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that…
We review existing approaches to mathematical modeling and analysis of multi-agent systems in which complex collective behavior arises out of local interactions between many simple agents. Though the behavior of an individual agent can be…
We present the MagNet, a neural network-based multi-agent interaction model to discover the governing dynamics and predict evolution of a complex multi-agent system from observations. We formulate a multi-agent system as a coupled…