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.

scholarly journals Chaotic synchronization of two optical cavity modes in optomechanical systems

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Nan Yang ◽  
Adam Miranowicz ◽  
Yong-Chun Liu ◽  
Keyu Xia ◽  
Franco Nori
Keyword(s):  
Phase Synchronization ◽  
Optical Cavity ◽  
Chaotic Synchronization ◽  
Complete Synchronization ◽  
Optical Mode ◽  
Mechanical Resonator ◽  
Optomechanical System ◽  
Optomechanical Systems ◽  
Cavity Modes ◽  
Optical Modes

Abstract The synchronization of the motion of microresonators has attracted considerable attention. In previous studies, the microresonators for synchronization were studied mostly in the linear regime. While the important problem of synchronizing nonlinear microresonators was rarely explored. Here we present theoretical methods to synchronize the motions of chaotic optical cavity modes in an optomechanical system, where one of the optical modes is strongly driven into chaotic motion and transfers chaos to other weakly driven optical modes via a common mechanical resonator. This mechanical mode works as a common force acting on each optical mode, which, thus, enables the synchronization of states. We find that complete synchronization can be achieved in two identical chaotic cavity modes. For two arbitrary nonidentical chaotic cavity modes, phase synchronization can also be achieved in the strong-coupling small-detuning regime.

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

SYNCHRONIZING CHAOTIC ATTRACTORS OF CHUA'S CANONICAL CIRCUIT: THE CASE OF UNCERTAINTY IN CHAOS SYNCHRONIZATION

2006 ◽  
Vol 16 (07) ◽  
pp. 1961-1976 ◽  
Author(s):  
I. M. KYPRIANIDIS ◽  
A. N. BOGIATZI ◽  
M. PAPADOPOULOU ◽  
I. N. STOUBOULOS ◽  
G. N. BOGIATZIS ◽  
...  
Keyword(s):  
Coupling Strength ◽  
Chaos Synchronization ◽  
Phase Synchronization ◽  
Initial Conditions ◽  
Chaotic Synchronization ◽  
Chaotic Attractors ◽  
Coexisting Attractors

In this paper, we have studied the dynamics of two identical resistively coupled Chua's canonical circuits and have found that it is strongly affected by initial conditions, coupling strength and the presence of coexisting attractors. Depending on the coupling variable, chaotic synchronization has been observed both numerically and experimentally. Anti-phase synchronization has also been studied numerically clarifying some aspects of uncertainty in chaos synchronization.

STIMULUS-INDUCED CHAOTIC SYNCHRONIZATION OF CHUA'S OSCILLATORS

2006 ◽  
Vol 16 (10) ◽  
pp. 2843-2853
Author(s):  
V. V. KLINSHOV ◽  
V. B. KAZANTSEV ◽  
V. I. NEKORKIN
Keyword(s):  
Initial Phase ◽  
Chaotic Dynamics ◽  
Phase Synchronization ◽  
Cluster Formation ◽  
Time Moment ◽  
Chaotic Oscillation ◽  
Single Pulse ◽  
Chaotic Synchronization ◽  
Phase Reset ◽  
Chaotic Oscillators

The problem of phase synchronization of Chua's chaotic oscillators is investigated. We consider Chua's circuit when it exhibits a chaotic attractor and apply a single pulse stimulus. It is shown that under certain conditions the system displays self-referential phase reset (SPR) phenomenon. This is a case when the reset phase of the chaotic oscillation is independent on the initial phase, hence on the time moment when the stimulus has been applied. In an ensemble of chaotic oscillators simultaneously stimulated, the SPR yields mutual phase coherence or synchronization between the units. We describe basic dynamical mechanisms of the effect and show how it can be used for controllable cluster formation and for the control of chaotic dynamics.

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.

CHAOTIC SYNCHRONIZATION AND ANTISYNCHRONIZATION IN COUPLED SINE MAPS

2005 ◽  
Vol 15 (07) ◽  
pp. 2161-2177 ◽  
Author(s):  
V. L. MAISTRENKO ◽  
YU. L. MAISTRENKO ◽  
E. MOSEKILDE
Keyword(s):  
Parameter Space ◽  
Period Doubling ◽  
Chaotic Synchronization ◽  
Basins Of Attraction ◽  
Main Diagonal ◽  
Different Types ◽  
Regions Of Stability ◽  
The Individual ◽  
Period Doubling Bifurcations

This paper investigates different types of chaotic synchronization in a system of two coupled sine maps. Due to the bimodal nature of the individual map, there is a range of parameters in which two synchronized chaotic states coexist along the main diagonal. In certain parameter regions, various (regular or chaotic) asynchronous states coexist with the synchronized chaotic states, and the basins of attraction become quite complicated. We determine the regions of stability for the so-called principal cycles that arise through transverse period-doubling bifurcations of synchronized saddle cycles. Particular emphasis is paid to the occurrence of chaotic antisynchronization, the coexistence of antisynchronous chaotic states, and the presence of narrow regions of parameter space in which states of chaotic synchronization and antisynchronization exist simultaneously. For each of these cases we provide detailed pictures of the associated basin structures.

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 Feedback control modulation for controlling chaotic maps

2021 ◽  
Vol 26 (3) ◽  
pp. 419-439
Author(s):  
Roberta Hansen ◽  
Graciela A. González
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Periodic Orbits ◽  
Waiting Time ◽  
Control Parameter ◽  
Chaotic Maps ◽  
Noise Sensitivity ◽  
Control Methods ◽  
Unstable Periodic Orbits ◽  
Discrete Maps

Based on existing feedback control methods such as OGY and Pyragas, alternative new schemes are proposed for stabilization of unstable periodic orbits of chaotic and hyperchaotic dynamical systems by suitable modulation of a control parameter. Their performances are improved with respect to: (i) robustness, (ii) rate of convergences, (iii) reduction of waiting time, (iv) reduction of noise sensitivity. These features are analytically investigated, the achievements are rigorously proved and supported by numerical simulations. The proposed methods result successful for stabilizing unstable periodic orbits in some classical discrete maps like 1-D logistic and standard 2-D Hénon, but also in the hyperchaotic generalized n-D Hénon-like maps.

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