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

2011 ◽  
Vol 16 (9) ◽  
pp. 3770-3785 ◽  
Author(s):  
Jun Ma ◽  
Fan Li ◽  
Long Huang ◽  
Wu-Yin Jin
Keyword(s):  
Chaotic System ◽  
Phase Synchronization ◽  
Parameters Estimation ◽  
Complete Synchronization ◽  
Synchronization Phase

Permutation Entropy of State Transition Networks to Detect Synchronization

2020 ◽  
Vol 30 (10) ◽  
pp. 2050154 ◽  
Author(s):  
Zahra Shahriari ◽  
Michael Small
Keyword(s):  
Time Series ◽  
State Transition ◽  
Phase Synchronization ◽  
Permutation Entropy ◽  
Generalized Synchronization ◽  
Complete Synchronization ◽  
Network Graph ◽  
Dynamical Equations ◽  
Synchronization Phase ◽  
Low Sensitivity

The dynamic behavior of many physical, biological, and other systems, are organized according to the synchronization of chaotic oscillators. In this paper, we have proposed a new method with low sensitivity to noise for detecting synchronization by mapping time series to complex networks, called the ordinal partition network, and calculating the permutation entropy of that structure. We show that this method can detect different kinds of synchronization such as complete synchronization, phase synchronization, and generalized synchronization. In all cases, the estimated permutation entropy decreases with increased synchronization. This method is also capable of estimating the topology of the network graph from the time series, without knowledge of the dynamical equations of individual nodes. This approach has been applied for the two identical and nonidentical coupled Rössler systems, two nonidentical coupled Lorenz systems, and a ring of coupled Lorenz96 oscillators.

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

2003 ◽  
Vol 28 (12) ◽  
pp. 1013 ◽  
Author(s):  
Muhan Choi ◽  
K. V. Volodchenko ◽  
Sunghwan Rim ◽  
Won-Ho Kye ◽  
Chil-Min Kim ◽  
...  
Keyword(s):  
Phase Synchronization ◽  
Complete Synchronization ◽  
Nd:Yag Lasers

Routes to complete synchronization via phase synchronization in coupled nonidentical chaotic oscillators

2002 ◽  
Vol 66 (1) ◽  
Author(s):  
Sunghwan Rim ◽  
Inbo Kim ◽  
Pilshik Kang ◽  
Young-Jai Park ◽  
Chil-Min Kim
Keyword(s):  
Phase Synchronization ◽  
Complete Synchronization ◽  
Chaotic Oscillators

Remarks on the complete synchronization for the Kuramoto model with frustrations

2018 ◽  
Vol 16 (04) ◽  
pp. 525-563 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Hwa Kil Kim ◽  
Jinyeong Park
Keyword(s):  
Phase Synchronization ◽  
Kuramoto Model ◽  
Prototype Model ◽  
Frequency Synchronization ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Kuramoto Oscillators ◽  
Applicable Range ◽  
The Kuramoto Model ◽  
Complete Frequency

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.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

2018 ◽  
Vol 7 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Hamed Tirandaz
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Parameters Estimation ◽  
Control Law ◽  
Complete Control ◽  
Synchronization Problem ◽  
Control And Synchronization ◽  
Adaptive Control Law

Abstract Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

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

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.

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

2002 ◽  
Vol 7 (4) ◽  
pp. 215-229 ◽  
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.

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

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.

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