scholarly journals Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Pramana ◽  
2008 ◽  
Vol 70 (6) ◽  
pp. 1143-1151 ◽  
Author(s):  
P. Muruganandam ◽  
F. F. Ferreira ◽  
H. F. El-Nashar ◽  
H. A. Cerdeira
Keyword(s):  
Coupled Oscillators ◽  
Phase Synchronization ◽  
Analytical Calculation

TWOFOLD IMPACT OF DELAYED FEEDBACK ON COUPLED OSCILLATORS

2007 ◽  
Vol 17 (07) ◽  
pp. 2517-2530 ◽  
Author(s):  
OLEKSANDR V. POPOVYCH ◽  
VALERII KRACHKOVSKYI ◽  
PETER A. TASS
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Phase Synchronization ◽  
Threshold Value ◽  
Phase Oscillators ◽  
Intermediate Coupling ◽  
Rich Variety ◽  
Dynamical Regimes ◽  
The Impact

We present a detailed bifurcation analysis of desynchronization transitions in a system of two coupled phase oscillators with delay. The coupling between the oscillators combines a delayed self-feedback of each oscillator with an instantaneous mutual interaction. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. We show that an increase of the coupling strength between oscillators may lead to a loss of synchronization. Intriguingly, the delay has a twofold influence on the oscillations: synchronizing for small and intermediate coupling strength and desynchronizing if the coupling strength exceeds a certain threshold value. We show that the desynchronization transition has the form of a crisis bifurcation of a chaotic attractor of chaotic phase synchronization. This study contributes to a better understanding of the impact of time delay on interacting oscillators.

PHASE SYNCHRONIZATION OF LINEARLY AND NONLINEARLY COUPLED OSCILLATORS WITH INTERNAL RESONANCE

2009 ◽  
Vol 23 (30) ◽  
pp. 5715-5726
Author(s):  
YONG LIU
Keyword(s):  
Coupling Strength ◽  
Coupled Oscillators ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Phase Synchronization ◽  
Coupled Systems ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Phase Dynamics ◽  
Diffuse Clouds

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, it demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase in the linear coupling strength, the effect of phase synchronization between two sub-systems was enhanced, while increased firstly, and then decayed as nonlinear coupling strength increases. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the Lyapunov exponents, which can also be explained by the diffuse clouds.

scholarly journals Analytical Calculation of Power Flow in Three Coupled Oscillators and its Application to One Dimensional Crystal

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Chifu Ebene Ndikilar ◽  
Sofwan I. Saleh ◽  
Hafeez Yusuf Hafeez ◽  
Lawan Sani Taura
Keyword(s):  
White Noise ◽  
Coupled Oscillators ◽  
Power Flow ◽  
Equations Of Motion ◽  
Analytical Calculation ◽  
Asymptotic Value ◽  
One Dimensional ◽  
Two Systems ◽  
Dimensional Crystal ◽  
Equations Of Motions

The motion of a system consisting of three coupled oscillators of three masses attached together by four springs is studied analytically. The system is used as a model to describe the interactions between atoms in a one dimensional crystal with spring-like forces under white noise excitations.  Two different cases are considered and the frequencies of oscillations are obtained as well as the equations of motion.  The equations of motions are used to determine the power flow in the systems. The power flow determined is used to describe the effects of substitution impurities in a crystal. The power flow of the two systems studied decreases exponentially with increase in frequency to an asymptotic value.

scholarly journals Stochastic comparison of synchronization in activator- and repressor-based coupled gene oscillators

2021 ◽  
Author(s):  
Supravat Dey ◽  
A B M Shamim Ul Hasan ◽  
Abhyudai Singh ◽  
Hiroyuki Kurata
Keyword(s):  
Time Delay ◽  
Coupled Oscillators ◽  
Molecular Mechanisms ◽  
Phase Synchronization ◽  
Stochastic Comparison ◽  
Intercellular Coupling ◽  
Coupled Models ◽  
Coupling Delay ◽  
Coupling Time ◽  
Presence And Absence

Inside living cells, proteins or mRNA can show oscillations even without a periodic driving force. Such genetic oscillations are precise timekeepers for cell-cycle regulations, pattern formation during embryonic development in higher animals, and daily cycle maintenance in most organisms. The synchronization between oscillations in adjacent cells happens via intercellular coupling, which is essential for periodic segmentation formation in vertebrates and other biological processes. While molecular mechanisms of generating sustained oscillations are quite well understood, how do simple intercellular coupling produces robust synchronizations are still poorly understood? To address this question, we investigate two models of coupled gene oscillators - activator-based coupled oscillators (ACO) and repressor-based coupled oscillators (RCO) models. In our study, a single autonomous oscillator (that operates in a single cell) is based on a negative feedback, which is delayed by intracellular dynamics of an intermediate species. For the ACO model (RCO), the repressor protein of one cell activates (represses) the production of another protein in the neighbouring cell after a intercellular time delay. We investigate the coupled models in the presence of intrinsic noise due to the inherent stochasticity of the biochemical reactions. We analyze the collective oscillations from stochastic trajectories in the presence and absence of explicit coupling delay and make careful comparison between two models. Our results show no clear synchronizations in the ACO model when the coupling time delay is zero. However, a non-zero coupling delay can lead to anti-phase synchronizations in ACO. Interestingly, the RCO model shows robust in-phase synchronizations in the presence and absence of the coupling time delay. Our results suggest that the naturally occurring intercellular couplings might be based on repression rather than activation where in-phase synchronization is crucial.

Effects of initial conditions and coupling competition modes on behaviors of coupled non-identical fractional-order bistable oscillators

2016 ◽  
Vol 94 (11) ◽  
pp. 1158-1166
Author(s):  
Liming Wang
Keyword(s):  
Boundary Layer ◽  
Monte Carlo ◽  
Fractional Order ◽  
Coupled Oscillators ◽  
Chaos Synchronization ◽  
Phase Synchronization ◽  
Initial Conditions ◽  
Coupled System ◽  
Amplitude Death ◽  
Dynamic Behaviors

The effects of the initial conditions and the coupling competition modes on the dynamic behaviors of coupled non-identical fractional-order bistable oscillators are investigated intensively and the various phenomena are explored. The coupled system can be controlled to form chaos synchronization, chaos anti-phase synchronization, amplitude death, oscillation death, etc., by setting the initial conditions or selecting the coupling competition modes. Depending on whether the arbitrary initial conditions can let two coupled oscillators stop oscillating, the dynamic behaviors of the coupled system are further classified into three types, that is, both of oscillators stop oscillating, only one oscillator stops oscillating, and none of oscillators stop oscillating. Based on the principle of Monte Carlo method, the percentages of three types of dynamic behaviors are calculated for the different coupling competition modes and the dynamic behaviors of the coupled system are characterized from the perspective of statistics. Moreover, the mechanism behind the various phenomena is explained in detail by the concept of boundary layer and the optimum coupling competition modes are found.

EMBEDDED MOVING SADDLE POINT AND ITS RELATION TO TURBULENCE IN FLUIDS AND PLASMAS

2004 ◽  
Vol 18 (13) ◽  
pp. 1805-1843 ◽  
Author(s):  
KAIFEN HE
Keyword(s):  
Saddle Point ◽  
Coupled Oscillators ◽  
Review Paper ◽  
Phase Synchronization ◽  
Special Kind ◽  
Spatiotemporal Chaos ◽  
Critical Event ◽  
Steady Wave ◽  
Self Organized ◽  
Motion Characteristic

Hysteresis is a common phenomenon in a type of nonlinear waves. Corresponding to the negative tangential branch of a hysteretic curve the steady wave solutions are unstable due to saddle instability; such a saddle steady wave (SSW) is a moving saddle point in the system. In a model system based on a nonintegrable equation derived in fluid and plasma physics, a clear connection is found between turbulent solutions and the appearance of hystereses. A physical cause underlying this phenomenon is the embedded saddle point. In this review paper we focus on a senario of strong turbulent motion that is related to the saddle point. It is shown that in the reference frame moving with the SSW the nonlinear wave can be transformed into a set of coupled oscillators for which the SSW provides a potential; when the orbit of the oscillators collides with the saddle point a crisis onsets; subsequently occurs another critical event during which the master oscillator gets free from the trapping of the potential, inducing a transition to spatiotemporal chaos. The turbulent state after the transition is actually a special kind of self-organized motion characteristic by on-off imperfect phase synchronization among these oscillators.

scholarly journals Phase synchronization of fluid-fluid interfaces as hydrodynamically coupled oscillators

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Eujin Um ◽  
Minjun Kim ◽  
Hyoungsoo Kim ◽  
Joo H. Kang ◽  
Howard A. Stone ◽  
...  
Keyword(s):  
Coupled Oscillators ◽  
Phase Synchronization ◽  
Feedback Mechanism ◽  
Immiscible Fluids ◽  
Droplet Breakup ◽  
Fluid Interfaces ◽  
Two Phase ◽  
Negative Feedback Mechanism ◽  
Characteristic Oscillation ◽  
Complete Set

Abstract Hydrodynamic interactions play a role in synchronized motions of coupled oscillators in fluids, and understanding the mechanism will facilitate development of applications in fluid mechanics. For example, synchronization phenomenon in two-phase flow will benefit the design of future microfluidic devices, allowing spatiotemporal control of microdroplet generation without additional integration of control elements. In this work, utilizing a characteristic oscillation of adjacent interfaces between two immiscible fluids in a microfluidic platform, we discover that the system can act as a coupled oscillator, notably showing spontaneous in-phase synchronization of droplet breakup. With this observation of in-phase synchronization, the coupled droplet generator exhibits a complete set of modes of coupled oscillators, including out-of-phase synchronization and nonsynchronous modes. We present a theoretical model to elucidate how a negative feedback mechanism, tied to the distance between the interfaces, induces the in-phase synchronization. We also identify the criterion for the transition from in-phase to out-of-phase oscillations.

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