Related papers: Optimal synchronisation to a limit cycle
Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronisation of a Li\'enard system to its limit cycle using a bounded external force. To tackle…
The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase…
Classical self-sustained oscillators, that generate periodic motion without periodic external forcing, are ubiquitous in science and technology. The realization of nonclassical self-oscillators is an important goal of quantum physics. We…
A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz.…
Recently, several studies have investigated synchronization in quantum-mechanical limit-cycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillator's phase was overdamped…
Synchronization is a major concept in nonlinear physics. In a large number of systems, it is observed at long times for a sinusoidal excitation. In this paper, we design a transiently non-sinusoidal driving to reach the synchronization…
The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodical force is combined with a theoretical analysis by means of the quasi-harmonic…
Limit cycles (attractors for neighbouring periodic orbits in a dissipative dynamical system) have been widely studied but the corresponding generalization for quasi periodic orbits have rarely been discussed. Here we investigate "higher…
We develop an analytical framework to study the synchronization of a quantum self-sustained oscillator to an external signal. Our unified description allows us to identify the resource on which quantum synchronization relies, and to compare…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
To observe synchronization in a large network of classical or quantum systems demands both excellent control of the interactions between the nodes and very accurate preparation of the initial conditions due to the involved nonlinearities…
We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered.…
We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a…
Synchronization of forced reactively coupled van der Pol oscillators is investigated in the phase approximation. We discuss essential features of the reactive coupling. Bifurcation mechanisms for the destruction of complete synchronization…
Limit-cycle oscillators are the basic building blocks for synchronization; yet, the notion of a quantum limit cycle has remained unclear. Here, we study quantum limit cycles and synchronization in the presence of continuous heterodyne…
A new method is presented for the analysis of limit cycle oscillations in mixed-feedback systems. The calculation of the limit cycle is reformulated as the zero finding of a mixed-monotone relation, that is, of the difference of two…
Recently, the synchronization of coupled quantum oscillators has attracted a great deal of interest. Synchronization requires driven constituents, and in such systems, the coupling can be designed to be nonreciprocal. Nonreciprocally…
We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained…
Nonlinear oscillators are commonly encountered in a wide range of physical and engineering systems, exhibiting rich and complex dynamics. Among these, the Van der Pol oscillator is well known for its self-sustained limit cycle behavior.…
This paper proposes a novel method to achieve and preserve synchronization for a set of connected heterogeneous Van der Pol oscillators. Unlike the state-of-the-art synchronization methods, in which a large coupling gain is applied to…