相关论文: Analyzing Parametric Oscillator Ising Machines thr…
We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian Mean Field (HMF) model. Our numerical results support the connection…
Interest in non-algorithmic, unconventional computing is rising in recent years due to more and more apparent short comings of classic stored-program digital computers, such as energy efficiency, degree of parallelism in computations, clock…
We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase…
We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
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…
Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
We study systems of Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional regular topologies like linear chains, rings, hypercubic lattices and Cayley-trees. For the special cases of next-neighbor and infinite-range…
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original,…
A coherent Ising machine (CIM) is known to deliver the low-energy states of the Ising model. Here, we investigate how well the CIM simulates the thermodynamic properties of a two-dimensional square-lattice Ising model. Assuming that the…
A non-equilibrium open-dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial…
Many combinatorial problems can be mapped to Ising machines, i.e., networks of coupled oscillators that settle to a minimum-energy ground state, from which the problem solution is inferred. This work proposes DROID, a novel event-driven…
We consider the Kuramoto model of globally coupled phase oscillators in its continuum limit, with individual frequencies drawn from a distribution with density of class $C^n$ ($n\geq 4$). A criterion for linear stability of the uniform…
Controlling the behavior of nonlinear systems on networks is a paramount task in control theory, in particular the control of synchronization, given its vast applicability. In this work, we focus on pinning control and we examine two…
This paper presents a nonlinear control framework for steering networks of coupled oscillators toward desired phase-locked configurations. Inspired by brain dynamics, where structured phase differences support cognitive functions, the focus…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
Cluster states are versatile quantum resources and an essential building block for measurement-based quantum computing. The possibility to generate cluster states in specific systems may thus serve as an indicator regarding if and to what…
Solving intractable mathematical problems in simulators composed of atoms, ions, photons or electrons has recently emerged as a subject of intense interest. Here we extend this concept to phonons that are localised in spectrally pure…
A coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs), in which the "strongest" collective mode of oscillation at well above threshold corresponds to an optimum solution of a given Ising problem. When a pump…