Related papers: The size of the sync basin resolved
We design a quasi-one dimensional spin chain with engineered coupling strengths such that the natural dynamics of the spin chain evolves a single excitation localized at the left hand site to any specified single particle state on the whole…
Previous results have shown that a large class of complex systems consisting of many interacting heterogeneous phase oscillators exhibit an attracting invariant manifold. This result has enabled reduced analytic system descriptions from…
We consider an infinite network of globally-coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when…
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…
The dynamics of an infinite system of point particles in $\mathbb{R}^d$, which hop and interact with each other, is described at both micro- and mesoscopic levels. The states of the system are probability measures on the space of…
This paper studies the winding of a continuously differentiable Gaussian stationary process $f:\mathbb{R}\to\mathbb{C}$ in the interval $[0,T]$. We give formulae for the mean and the variance of this random variable. The variance is shown…
QCD-like theories can be engineered to remain in a confined phase when compactified on an arbitrarily small circle, where their features may be studied quantitatively in a controlled fashion. Previous work has elucidated the generation of a…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
To sensitively test scaling in the 2D XY model quenched from high-temperatures into the ordered phase, we study the difference between measured correlations and the (scaling) results of a Gaussian-closure approximation. We also directly…
We study a population of swarmalators (swarming/mobile oscillators) which run on a ring and are subject to random pinning. The pinning represents the tendency of particles to stick to defects in the underlying medium which competes with the…
We study feedback control of twisted states in the Kuramoto model (KM) of identical oscillators defined on deterministic nearest neighbor graphs containing complete simple ones when it may have phase-lag. Bifurcations of such twisted…
Over the past decades chimera states have attracted considerable attention given their unexpected symmetry-breaking spatio-temporal nature, simultaneously exhibiting synchronous and incoherent behaviours under specific conditions. Despite…
We identify the large-$N$ scaling of the metrological quantum gain offered by over-squeezed spin states that are accessible by one-axis-twisting, as a function of the preparation time. We further determine how the scaling is modified by…
We study bifurcations of twisted solutions in a continuum limit (CL) for the Kuramoto model (KM) of identical oscillators defined on nearest neighbor graphs, which may be deterministic dense, random dense or random sparse, when it may have…
The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the generalized Hill problem. The parametric variation of the position and the linear stability of the equilibrium points is…
We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a…
We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the…
The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a…
We investigate the finite-size effects on the dynamical evolution of the Kuramoto model with inertia coupled through triadic interactions. Our findings reveal that fluctuations resulting from the finite size drive the system toward a…
Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize the riddled basin using the uncertainty…