Using three coupled harmonic oscillators, we propose a quantum approach without using qubits to efficiently factorize an integer with only three steps. These three harmonic oscillators are coupled together via nonlinear interactions. This factoring method can be applied even if two harmonic oscillators are prepared in mixed states. As simple examples, we show how to factorize N = 15 and 35 usin...

Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization crucial to our understanding various nonlinear systems, ranging from biological functions electrical engineering. On another front, in condensed matter physics, topology utilized realize properties like topological edge modes, as demonstrated by celebrated insulators. Here, we integ...

This topical issue collects contributions of recent achievements and scientific progress related to the collective behavior nonlinear dynamical oscillators. The individual papers focus on different questions present-day interest in this topic.

We describe a transition from fully synchronous periodic oscillations to partially synchronous quasiperiodic dynamics in ensembles of identical oscillators with all-to-all coupling that nonlinearly depends on the generalized order parameters. We present an analytically solvable model that predicts a regime where the mean field does not entrain individual oscillators, but has a frequency incomme...

The problem of natural wave control involves steering a lattice of oscillators towards a desired natural (i.e. zero-input) assignment of energy and phase across the lattice. This problem is formulated and solved for lattices of linear oscillators via a passivity-based approach. Numerical simulations of 1D and 2D linear lattices and a 1D lattice of nonlinear oscillators confirm the effectiveness...

The collective phase response to a macroscopic external perturbation of a population of interacting nonlinear elements exhibiting collective oscillations is formulated for the case of globally coupled oscillators. The macroscopic phase sensitivity is derived from the microscopic phase sensitivity of the constituent oscillators by a two-step phase reduction. We apply this result to quantify the ...

Voltage-controlled oscillators are widely used circuit blocks, particularly in phase-locked loops. As CMOS is the technology of choice for many applications, CMOS oscillators with low phase noise and timing jitter are highly desired. CMOS ring oscillators with five different delay cell topologies have been designed, fabricated and evaluated for phase noise performance. Our results show that rin...

This paper treats the synchronization of a chain of non linear and uncertain model of non identical oscillators. Using the Lyapunov theory of stability, a dynamical controller guarantying the oscillators synchronization is determined. The problem of synchronization is transformed in a problem of asymptotic stabilization for a nonlinear system and then is formulated as a system of linear matrix ...