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Related Experiment Video

Updated: May 18, 2026

Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

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Published on: June 9, 2023

Design of coupling for synchronization in time-delayed systems.

Dibakar Ghosh¹, Ioan Grosu, Syamal K Dana

¹Department of Mathematics, University of Kalyani, West Bengal 741235, India.

Chaos (Woodbury, N.Y.)

|October 2, 2012

Summary

We designed delay coupling to achieve various synchronization types in dynamical systems, including mixed synchronization. This method allows controlling attractor sizes and ensures stability for mismatched oscillators.

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Area of Science:

Nonlinear dynamics
Complex systems
Chaos theory

Background:

Delay dynamical systems exhibit complex behaviors.
Synchronization phenomena are crucial in various scientific fields.
Controlling synchronization in mismatched oscillators remains challenging.

Purpose of the Study:

To design a delay coupling method for achieving diverse synchronization patterns.
To enable control over attractor sizes in different synchronization regimes.
To investigate mixed synchronization where different states synchronize and antisynchronize.

Main Methods:

Development of a novel delay coupling strategy.
Application of Krasovskii-Lyapunov function theory for stability analysis.
Utilizing the Hurwitz matrix criterion for stability assessment.
Numerical simulations on Mackey-Glass and delay Rössler systems.

Main Results:

Successfully targeted synchronization, antisynchronization, lag- and antilag-synchronization, and amplitude death.
Achieved control over attractor size scaling across different synchronization regimes.
Demonstrated a novel mixed synchronization pattern with coexisting synchronization and antisynchronization.
Validated stability conditions for synchronization.

Conclusions:

The proposed delay coupling design offers a versatile approach to controlling synchronization in delay dynamical systems.
The method provides a means to achieve complex synchronization patterns, including mixed synchronization.
Stability analysis confirms the robustness of the synchronization regimes.