Related papers: Phase autoencoder for limit-cycle oscillators
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for…
Phase synchronization was proved to be unbounded in quantum level, but the witness of phase synchronization is always expensive in terms of the quantum resource and non-local measurements involved. Based on the quantum uncertainty relation,…
The asymptotic behavior at infinity of oscillatory integrals is in detail investigated by using the Newton polyhedra of the phase and the amplitude. We are especially interested in the case that the amplitude has a zero at a critical point…
We report the observation of a novel and non-trivial synchronization state in a system consisting of three oscillators coupled in a linear chain. For certain ranges of coupling strength the weakly coupled oscillator pair exhibits phase…
We study collective behavior of locally-coupled limit-cycle oscillators with scattered intrinsic frequencies on $d$-dimensional lattices. A linear analysis shows that the system should be always desynchronized up to $d=4$. On the other…
We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…
Oscillators have two main limitations: their synchronization properties are limited (i.e they have a finite synchronization region) and they have no memory of past interactions (i.e. they return to their intrinsic frequency whenever the…
We investigate a system of four nearest neighbour bidirectional coupled phase oscillators of dissimilar initial frequencies in a ring at the changeover into a synchronizing state. There are twenty four permutations upon assigning the…
As to methods for expanding an oscillatory integral into an asymptotic series with respect to the parameter, the method of stationary phase for the non-degenerate phases and the method of using resolution of singularities for degenerate…
Phase reduction is an effective theoretical and numerical tool for studying synchronization of coupled deterministic oscillators. Stochastic oscillators require new definitions of asymptotic phase. The $Q$-function, i.e. the slowest…
Neural encoding of objects and cognitive states remains an elusive yet crucial aspect of brain function. While traditional feed-forward machine learning neural networks have enormous potential to encode information, modern architectures…
We study the phase synchronization between collective rhythms of fully locked oscillator groups. For weakly interacting groups of two oscillators with global sinusoidal coupling, we analytically derive the collective phase coupling…
We present a method for analyzing the phase noise of oscillators based on feedback driven high quality factor resonators. Our approach is to derive the phase drift of the oscillator by projecting the stochastic oscillator dynamics onto a…
A system of two coupled ensembles of phase oscillators can follow different routes to inter-ensemble synchronization. Following a short report of our preliminary results [Phys. Rev. E. {\bf 78}, 025201(R) (2008)], we present a more detailed…
We introduce a simple model system to study synchronization theoretically in quantum oscillators that are not just in limit-cycle states, but rather display a more complex bistable dynamics. Our oscillator model is purely dissipative, with…
This paper is dedicated to control theoretically explainable application of autoencoders to optimal fault detection in nonlinear dynamic systems. Autoencoder-based learning is a standard machine learning method and widely applied for fault…
By spreading phases on the unit circle, desynchronization algorithm is a powerful tool to achieve round-robin scheduling, which is crucial in applications as diverse as media access control of communication networks, realization of…
Phase reduction framework for limit-cycling systems based on isochrons has been used as a powerful tool for analyzing rhythmic phenomena. Recently, the notion of isostables, which complements the isochrons by characterizing amplitudes of…
Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of…
A model of two self-sustained oscillators interacting through memristive coupling is studied. Memristive coupling is realized by using a cubic memristor model. Numerical simulation is combined with theoretical analysis by means of…