Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers

The synchronous dynamics of many limit-cycle oscillators can be described by phase models. The Kuramoto model serves as a prototype model for phase synchronization and has been extensively studied in the last 40 years. In this paper, we deal with the complete synchronization problem of the Kuramoto model with frustrations on a complete graph. We study the robustness of complete synchronization with respect to the network structure and the interaction frustrations, and provide sufficient frameworks leading to the complete synchronization, in which all frequency differences of oscillators tend to zero asymptotically. For a uniform frustration and unit capacity, we extend the applicable range of initial configurations for the complete synchronization to be distributed on larger arcs than a half circle by analyzing the detailed dynamics of the order parameters. This improves the earlier results [S.-Y. Ha, H. Kim and J. Park, Remarks on the complete frequency synchronization of Kuramoto oscillators, Nonlinearity 28 (2015) 1441–1462; Z. Li and S.-Y. Ha, Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia, Math. Models Methods Appl. Sci. 26 (2016) 357–382.] which can be applicable only for initial configurations confined in a half circle.

Download Full-text

Phase synchronization in coupled Nd:YAG lasers

Optics Letters ◽

10.1364/ol.26.001406 ◽

2001 ◽

Vol 26 (18) ◽

pp. 1406 ◽

Cited By ~ 22

Author(s):

K. V. Volodchenko ◽

V. N. Ivanov ◽

Sung-Huan Gong ◽

Muhan Choi ◽

Young-Jai Park ◽

...

Keyword(s):

Phase Synchronization ◽

Nd:Yag Lasers

Download Full-text

A Numerical and Analytical Study of Phase Synchronization in Coupled SC-CNN Based Non-Identical Chaotic Systems

Journal of Mountain Research ◽

10.51220/jmr.v16i2.33 ◽

2021 ◽

Vol 16 (2) ◽

Author(s):

H. Shameem Banu ◽

P.S. Sheik Uduman

Keyword(s):

Analytical Study ◽

Chaotic Systems ◽

Phase Synchronization ◽

Simulation Method ◽

Cellular Neural Network ◽

Phase Portraits ◽

Complete Synchronization ◽

Synchronous State ◽

Explicit Analytical Solution ◽

Proposed Model

This paper seeks to address the phase synchronization phenomenon using the drive-response concept, in our proposed model, State Controlled Cellular Neural Network (SC-CNN) based on variant of MuraliLakshmanan-Chua (MLCV) circuit. Using this unidirectionally coupled chaotic non autonomous circuits, we described the transition of unsynchronous to synchronous state, by numerical simulation method as well as the results are confirmed by solving explicit analytical solution. In this aspect, the system undergoes the new effect of phase synchronization (PS) phenomenon have been observed before complete synchronization (CS) state. To characterize these phenomena by the phase portraits and the time series plots. Also particularly characterize for PS by the method of partial Poincare section map using phase difference versus time, numerically and analytically. The study of dynamics involved in SC-CNN circuit systems, mainly applicable in the field of neurosciences and in telecommunication fields.

Download Full-text

In-phase and antiphase complete chaotic synchronization in symmetrically coupled discrete maps

Discrete Dynamics in Nature and Society ◽

10.1155/s1026022602000250 ◽

2002 ◽

Vol 7 (4) ◽

pp. 215-229 ◽

Cited By ~ 7

Author(s):

Vladimir Astakhov ◽

Alexey Shabunin ◽

Alexander Klimshin ◽

Vadim Anishchenko

Keyword(s):

Periodic Orbits ◽

Phase Synchronization ◽

Chaotic Synchronization ◽

Complete Synchronization ◽

Diffusive Coupling ◽

Discrete Maps ◽

Regions Of Stability ◽

Main Family

We consider in-phase and antiphase synchronization of chaos in a system of coupled cubic maps. Regions of stability and robustness of the regime of in-phase complete synchronization was found. It was demonstrated that the loss of the synchronization is accompanied by bubbling and riddling phenomena. The mechanisms of these phenomena are connected with bifurcations of the main family of periodic orbits and orbits appeared from them. We found that in spite of the in-phase synchronization, the antiphase self-synchronization of chaos is impossible for discrete maps with symmetric diffusive coupling. For achieving antiphase synchronization we used method of controlled synchronization by addition feedback. The region of the controlled antiphase synchronization and phenomena which accompany the loss of the synchronization are presented.

Download Full-text

Synchronization or cluster synchronization in coupled Van der Pol oscillators networks with different topological types

Physica Scripta ◽

10.1088/1402-4896/ac46f3 ◽

2021 ◽

Author(s):

Shuai Wang ◽

Yong Li

Keyword(s):

Periodic Solutions ◽

Phase Synchronization ◽

Van Der Pol Oscillator ◽

Cluster Synchronization ◽

Critical Conditions ◽

Complete Synchronization ◽

Van Der Pol ◽

Special Groups ◽

Different Types ◽

Van Der Pol Oscillators

Abstract In this paper, we try to discuss the mechanism of synchronization or cluster synchronization in the coupled Van der Pol oscillator networks with different topology types by using the theory of rotating periodic solutions. The synchronous solutions here are transformed into rotating periodic solutions of some dynamical systems. By analyzing the bifurcation of rotating periodic solutions, the critical conditions of synchronous solutions are given in three different networks. We use the rotating periodic matrix in the rotating periodic theory to judge various types of synchronization phenomena, such as complete synchronization, anti-phase synchronization, periodic synchronization, or cluster synchronization. All rotating periodic matrices which satisfy the exchange invariance of multiple oscillators form special groups in these networks. By using the conjugate classes of these groups, we obtain various possible synchronization solutions in the three networks. In particular, we find symmetry has different effects on synchronization in different networks. The network with better symmetry has more elements in the corresponding group, which may have more types of synchronous solutions. However, different types of symmetry may get the same type of synchronous solutions or different types of synchronous solutions, depending on whether their corresponding rotating periodic matrices are similar.

Download Full-text

Phase synchronization in coupled Nd:YAG lasers

2000 2nd International Conference. Control of Oscillations and Chaos. Proceedings (Cat. No.00TH8521) ◽

10.1109/coc.2000.874301 ◽

2002 ◽

Author(s):

V.N. Ivanov ◽

K.V. Volodchenko ◽

Sung-Huan Gong ◽

Muhan Choi ◽

Young-Jai Park ◽

...

Keyword(s):

Phase Synchronization ◽

Nd:Yag Lasers

Download Full-text

Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2010.12.030 ◽

2011 ◽

Vol 16 (9) ◽

pp. 3770-3785 ◽

Cited By ~ 63

Author(s):

Jun Ma ◽

Fan Li ◽

Long Huang ◽

Wu-Yin Jin

Keyword(s):

Chaotic System ◽

Phase Synchronization ◽

Parameters Estimation ◽

Complete Synchronization ◽

Synchronization Phase

Download Full-text

Transition of synchronization of coupled maps in modular networks

International Journal of Modern Physics C ◽

10.1142/s0129183120500114 ◽

2019 ◽

Vol 31 (01) ◽

pp. 2050011

Author(s):

Bin Zhang ◽

Ru-Hai Du ◽

Sheng-Jun Wang ◽

Shi-Xian Qu

Keyword(s):

Coupling Strength ◽

Phase Synchronization ◽

Spatiotemporal Chaos ◽

Spatiotemporal Patterns ◽

Cluster Synchronization ◽

Complete Synchronization ◽

Modular Networks ◽

Fully Connected ◽

Fully Connected Networks ◽

Ordered State

Spatiotemporal patterns in the transition of phase synchronization in modular networks of coupled logistic maps are studied. The phase diagram of spatiotemporal patterns is presented by analyzing both the collective behavior of direction-phase and the changes of links connecting clusters of different phases. The spatiotemporal chaos is obtained when the coupling strength is weak. We show that the spatiotemporal chaos can be composed by clusters in periodic states. The region of periodic behaviors is independent of modularity. Then with decreasing coupling or increasing modularity, the system presents the same transition path from complete synchronization to cluster synchronization, except the network is close to fully connected networks. There are two distinctive scenarios from disordered behavior to an ordered state when the modularity ratio varies from one to zero. First, for networks with small modularity, the number of phase synchronized clusters decreases with the increasing of the coupling strength. Second, for networks with large modularity, the number of phase-synchronized clusters nonmonotonically changes with the coupling strength.

Download Full-text

Synchronization Dynamics of Two Heterogeneous Chaotic Rulkov Neurons with Electrical Synapses

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127417300099 ◽

2017 ◽

Vol 27 (02) ◽

pp. 1730009 ◽

Cited By ~ 4

Author(s):

Lifang Cheng ◽

Hongjun Cao

Keyword(s):

Phase Synchronization ◽

Spiking Neurons ◽

Flip Bifurcation ◽

Quiescent State ◽

Complete Synchronization ◽

Electrical Synapses ◽

Bursting Neurons ◽

Inhibitory Coupling ◽

Burst Synchronization ◽

Firing Neuron

Two heterogeneous chaotic Rulkov neurons with electrical synapses are investigated in this paper. First, we study the ability of the second neuron to modify the dynamics of the first neuron. It is shown that when the parameters of the first neuron are located at the vicinity of the Neimark–Sacker bifurcation curves the first firing neuron can be controlled into the quiescent state when coupled with the second neuron. While the parameters of the first neuron are near the flip bifurcation curves the first firing neuron cannot be suppressed. Second, we discuss burst synchronization for two bursting neurons and two tonic spiking neurons. It is shown that two heterogeneous chaotic Rulkov neurons with tonic spiking firing cannot reach anti-phase synchronization under the inhibitory coupling, which is different from the property of nonchaotic Rulkov neurons. Finally, we show that for two bursting neurons if the coupling is strong enough then burst synchronization can be converted into spike synchronization. However, complete synchronization cannot be achieved for any strong coupling.

Download Full-text