scholarly journals Instantaneous phase synchronization of two decoupled quantum limit-cycle oscillators induced by conditional photon detection

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Yuzuru Kato ◽  
Hiroya Nakao
Keyword(s):  
Limit Cycle ◽  
Phase Synchronization ◽  
Quantum Limit ◽  
Photon Detection ◽  
Instantaneous Phase

scholarly journals Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2188
Author(s):  
Yuzuru Kato ◽  
Jinjie Zhu ◽  
Wataru Kurebayashi ◽  
Hiroya Nakao
Keyword(s):  
Limit Cycle ◽  
Operator Theory ◽  
Quantum Limit ◽  
Koopman Operator ◽  
Excitable Systems ◽  
Fundamental Quantity ◽  
Stochastic Oscillators ◽  
Semiclassical Regime ◽  
Deterministic Limit ◽  
Asymptotic Phase

The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for classical and semiclassical stochastic oscillators in a natural and unified manner by using the eigenfunctions of the Koopman operator of the system. We show that the proposed definition gives appropriate values of the phase and amplitude for strongly stochastic limit-cycle oscillators, excitable systems undergoing noise-induced oscillations, and also for quantum limit-cycle oscillators in the semiclassical regime.

scholarly journals Inferring Functional Neural Connectivity with Phase Synchronization Analysis: A Review of Methodology

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Junfeng Sun ◽  
Zhijun Li ◽  
Shanbao Tong
Keyword(s):  
Functional Connectivity ◽  
Phase Synchronization ◽  
Significance Test ◽  
Neural Connectivity ◽  
Neural Signals ◽  
Instantaneous Phase ◽  
Neuroscience Research ◽  
Observational Noise ◽  
Relationship Of ◽  
The Relationship

Functional neural connectivity is drawing increasing attention in neuroscience research. To infer functional connectivity from observed neural signals, various methods have been proposed. Among them, phase synchronization analysis is an important and effective one which examines the relationship of instantaneous phase between neural signals but neglecting the influence of their amplitudes. In this paper, we review the advances in methodologies of phase synchronization analysis. In particular, we discuss the definitions of instantaneous phase, the indexes of phase synchronization and their significance test, the issues that may affect the detection of phase synchronization and the extensions of phase synchronization analysis. In practice, phase synchronization analysis may be affected by observational noise, insufficient samples of the signals, volume conduction, and reference in recording neural signals. We make comments and suggestions on these issues so as to better apply phase synchronization analysis to inferring functional connectivity from neural signals.

DYNAMICS OF COLLECTIVE MULTI-STABILITY IN MODELS OF MULTI-UNIT NEURONAL SYSTEMS

2014 ◽  
Vol 24 (02) ◽  
pp. 1430004 ◽  
Author(s):  
MARC KOPPERT ◽  
STILIYAN KALITZIN ◽  
DEMETRIOS VELIS ◽  
FERNANDO LOPES DA SILVA ◽  
MAX A. VIERGEVER
Keyword(s):  
Limit Cycle ◽  
Analytical Model ◽  
Computational Models ◽  
Phase Synchronization ◽  
Neuronal Model ◽  
Model Type ◽  
Single Output ◽  
Patterns Of Behavior ◽  
Set Up ◽  
Neuronal Systems

In this study, we investigate the correspondence between dynamic patterns of behavior in two types of computational models of neuronal activity. The first model type is the realistic neuronal model; the second model type is the phenomenological or analytical model. In the simplest model set-up of two interconnected units, we define a parameter space for both types of systems where their behavior is similar. Next we expand the analytical model to two sets of 90 fully interconnected units with some overlap, which can display multi-stable behavior. This system can be in three classes of states: (i) a class consisting of a single resting state, where all units of a set are in steady state, (ii) a class consisting of multiple preserving states, where subsets of the units of a set participate in limit cycle, and (iii) a class consisting of a single saturated state, where all units of a set are recruited in a global limit cycle. In the third and final part of the work, we demonstrate that phase synchronization of units can be detected by a single output unit.

CHAOTIC PHASE SYNCHRONIZATION AND ITS BREAKDOWN - MAPPING MODEL AND CRITICAL DYNAMICS

2007 ◽  
Vol 21 (23n24) ◽  
pp. 3909-3917 ◽  
Author(s):  
HIROKAZU FUJISAKA ◽  
NAOFUMI TSUKAMOTO ◽  
SATOKI UCHIYAMA
Keyword(s):  
Limit Cycle ◽  
Phase Synchronization ◽  
Critical Dynamics ◽  
Coupled Oscillator ◽  
Chaotic Oscillators ◽  
Mapping Model ◽  
Phase Map ◽  
Coupled Oscillator Systems

In the present paper, we briefly discuss the construction of mapping model of coupled oscillator systems for limit-cycle oscillators and chaotic oscillators. A comparison of the proposed mapping model and other models, i.e., the Ikeda map and the phase map model is made. Furthermore, the critical dynamics associated with the breakdown of chaotic phase synchronization based on the present mapping model is discussed.

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