Related papers: Cooperative stabilization of persistent currents i…
Persistent currents in Bose condensates with a scalar order parameter are stabilized by the topology of the order parameter manifold. In condensates with multicomponent order parameters it is topologically possible for supercurrents to…
Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…
Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order…
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…
We investigate the stability of spatially uniform solutions for the collisionless dynamics of a fermionic superfluid. We demonstrate that, if the system size is larger than the superfluid coherence length, the solution characterized by a…
Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the…
In this paper, we propose an $N$ oscillators Kuramoto model with quaternions $\mathbb{H}$. In case the coupling strength is strong, a sufficient condition of synchronization is established for general $N\geqslant 2$. On the other hand, we…
In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…
We study Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional regular topologies with nearest neighbor interactions. We derive the analytical expressions for the common frequency in the case of phase-locked motion and for the…
We present a case study of how topology can affect synchronization. Specifically, we consider arrays of phase oscillators coupled in a ring or a chain topology. Each ring is perfectly matched to a chain with the same initial conditions and…
A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability…
Recent experiments in one and two-dimensional microfluidic arrays of droplets containing Belousov -Zhabotinsky reactants show a rich variety of spatial patterns [J. Phys. Chem. Lett. 1, 1241-1246 (2010)]. The dominant coupling between these…
We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…
A central mechanism of linearised two dimensional shear instability can be described in terms of a nonlinear, action-at-a-distance, phase-locking resonance between two vorticity waves which propagate counter to their local mean flow as well…
We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by combining the real-space dynamical mean-field theory with a two-site impurity solver. By calculating the local particle density and the pair…
Synchronization processes in populations of identical networked oscillators are in the focus of intense studies in physical, biological, technological and social systems. Here we analyze the stability of the synchronization of a network of…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…
We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…