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We present analytical investigation of exact lag synchronization between two unidirectionally coupled identical time delay systems with two characteristic delay times, where the delay time in the coupling is different from the delay time in…

Chaotic Dynamics · Physics 2007-05-23 E. M. Shahverdiev , S. Sivaprakasam , K. A. Shore

We study a model for two lasers that are mutually coupled opto-electronically by modulating the pump of one laser with the intensity deviations from the steady-state output of the other. Such a model is analogous to the equations describing…

Chaotic Dynamics · Physics 2024-10-30 E. M. Shahverdiev , P. A. Bayramov , K. A. Shore

In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…

Adaptation and Self-Organizing Systems · Physics 2018-03-30 David J. Jörg , Luis G. Morelli , Saúl Ares , Frank Jülicher

Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…

Chaotic Dynamics · Physics 2007-05-23 D. V. Senthilkumar , M. Lakshmanan

We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…

Pattern Formation and Solitons · Physics 2007-05-23 Vanessa Casagrande , Alexander S. Mikhailov

The remote synchronization of oscillators is essential for improving the performance, efficiency, and reliability of various systems and technologies, ranging from everyday telecommunications to cutting-edge scientific research and emerging…

The mechanism of synchronization of oscillations in two identical coupled flow systems has beenstudied. The time (past the coupling onset) during which a synchronous oscillation regime is establisheddepends on the oscillation phase…

Chaotic Dynamics · Physics 2015-06-26 A. A. Koronovskii , A. E. Hramov , I. A. Khromova

We consider the time required for complete synchronization of two identical one-way coupled vander Pol-Duffing oscillators occurring in the regime of dynamic chaos. The influence of the initial phase differ-ence between oscillators on the…

Chaotic Dynamics · Physics 2015-06-26 A. A. Koronovskii , A. E. Hramov , I. A. Khromova

Zero-lag synchronization (ZLS) is achieved in a very restricted mutually coupled chaotic systems, where the delays of the self-coupling and the mutual coupling are identical or fulfil some restricted ratios. Using a set of multiple…

Chaotic Dynamics · Physics 2008-11-26 Meital Zigzag , Maria Butkovski , Anja Englert , Wolfgang Kinzel , Ido Kanter

Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…

Dynamical Systems · Mathematics 2020-07-08 Reyk Börner , Paul Schultz , Benjamin Ünzelmann , Deli Wang , Frank Hellmann , Jürgen Kurths

We investigate chaos antisynchronization between two uni-directionally coupled multiple time delay power systems.The results are of certain importance to prevent power black-out in the entire power grid.

Chaotic Dynamics · Physics 2010-08-24 E. M. Shahverdiev

We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external…

chao-dyn · Physics 2009-10-28 Michael E. Bleich , Joshua E. S. Socolar

The dynamics of coupled Stuart-Landau oscillators play a central role in the study of synchronization phenomena. Previous works have focused on linearly coupled oscillators in different configurations, such as all-to-all or generic complex…

Pattern Formation and Solitons · Physics 2026-03-30 Wilfried Segnou , Riccardo Muolo , Marie Dorchain , Hiroya Nakao , Timoteo Carletti

We report the first experimental evidence of a successful synchronization of spatiotemporal chaos. The experiments were performed on two unidirectionally coupled, nonlinear-optical systems of single-feedback type. The synchronization was…

Pattern Formation and Solitons · Physics 2009-11-10 R. Neubecker , B. Guetlich

This article is concerned with the integration of the time-dependent Ginzburg-Landau (TDGL) equations of superconductivity. Four algorithms, ranging from fully explicit to fully implicit, are presented and evaluated for stability, accuracy,…

Numerical Analysis · Mathematics 2025-10-20 D. O. Gunter , H. G. Kaper , G. K. Leaf

Generalized synchronization (GS) describes a state in which two coupled dynamical systems exhibit a functional relationship between their variables. GS can be achieved by appropriately designing the coupling to constrain the dynamics onto…

Chaotic Dynamics · Physics 2025-03-19 Tania Ghosh , Soumitro Banerjee

A mutual synchronization of spin-torque oscillators coupled through current injection is studied theoretically. Models of electrical coupling in parallel and series circuits are proposed. Solving the Landau-Lifshitz-Gilbert equation,…

Mesoscale and Nanoscale Physics · Physics 2017-12-14 Tomohiro Taniguchi , Sumito Tsunegi , Hitoshi Kubota

In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling…

Adaptation and Self-Organizing Systems · Physics 2019-09-24 Viktor Novičenko , Irmantas Ratas

We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and…

Chaotic Dynamics · Physics 2015-05-13 Jie Sun , Erik M. Bollt , Takashi Nishikawa

A pair of coupled erbium doped fiber ring lasers is used to explore the dynamics of coupled spatiotemporal systems. The lasers are mutually coupled with a coupling delay less than the cavity round-trip time. We study synchronization between…

Chaotic Dynamics · Physics 2009-11-11 L. B. Shaw , I. B. Schwartz , E. A. Rogers , R. Roy