Phase locking of two limit cycle oscillators with delay coupling

Noise-Induced Quantum Synchronization

Synchronization is a widespread phenomenon in science and technology. Here, we study noise-induced synchronization in a quantum spin chain subjected to local Gaussian white noise. We demonstrate stable (anti)synchronization between the endpoint magnetizations of a quantum XY model with transverse field of arbitrary length. Remarkably, we show that noise applied to a single spin suffices to reach stable (anti)synchronization, and find that the two synchronized end spins are entangled. We additionally determine the optimal noise amplitude that leads to the fastest synchronization along the chain, and further compare the optimal synchronization speed to the fundamental Lieb-Robinson bound for information propagation.

Theory of Peer-to-Peer Locking of High-Power Gyrotron Oscillators Coupled with Delay

Peer-to-peer locking is a promising way to combine the power of high-power microwave oscillators. The peer-to-peer locking of gyrotrons is especially important because arrays of coupled gyrotrons are of special interest for fusion and certain other applications. However, in case of coupled microwave oscillators, the effect of delay in coupling is very significant and should be taken into account. In this article, we present the model of two delay-coupled gyrotrons. We develop an approximate theory of phase locking based on the generalized Adler’s equation, which allows for the treatment of in-phase and anti-phase locking modes. We also present a more rigorous bifurcation analysis of phase locking by using XPPAUT software under the limitation of small delay time. The structure of the phase-locking domains on the frequency-mismatch–coupling-strength plane of parameters is examined. Finally, we verify the results by numerical simulations in the case of finite delay time. The simulations reveal various regimes, including peer-to-peer locking, the suppression of one gyrotron by another, as well as the excitation of one gyrotron by another.

Bifurcation analysis of multistability of synchronous states in the system of two delay-coupled oscillators

Systems of mutually coupled oscillators with delay coupling are of great interest for various applications in electronics, laser physics, biophysics, etc. Time delay usually originates from the finite speed of propagation of the coupling signal. In this paper, we present the results of detailed bifurcation analysis of two delay-coupled limit-cycle (Landau-Stuart) oscillators. First, we study the simplified case when the delay time is much smaller than the oscillation build-up time. When the coupling signal propagates between the two counterparts, it acquires a phase shift, which strongly affects the synchronization pattern. Depending on this phase shift, the system may demonstrate the behavior typical for either dissipative or conservative (reactive) coupling. We examine stability of the in-phase and anti-phase synchronous states and reveal the complicated pattern of the synchronization domains on the frequency mismatch-coupling strength parameter plane paying a special attention to the mechanisms of appearance and disappearance of the phase multistability. We demonstrate that taking into account reactive phase nonlinearity the coupling signal acquires an additional phase shift, which depends on the signal intensity. We also examine the more complicated case of finite delay time. The increase of the reactive nonlinearity parameter and the delay time leads to transformations of synchronization domains similar to those that occur when the phase shift increases. For the bifurcation analysis, we employ XPPAUT and DDEBifTool package and verify the results by direct numerical integration.