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

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Quantifying the synchronizability of externally driven oscillators.

Andrzej Stefański¹

¹Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland.

Chaos (Woodbury, N.Y.)

|April 2, 2008

Summary

This study introduces a new method for estimating Lyapunov exponents to analyze synchronization in coupled oscillator systems. It enhances understanding of generalized synchronization with chaotic driving signals.

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Area of Science:

Nonlinear Dynamics
Chaos Theory
Complex Systems

Background:

Coupled oscillator systems exhibit complex behaviors like synchronization.
Generalized synchronization occurs between driving signals and response oscillators.
Irregular driving signals (chaotic or stochastic) pose challenges for synchronization analysis.

Purpose of the Study:

To analyze complete and generalized synchronization in externally driven oscillator arrays.
To investigate synchronization phenomena with irregular driving signals acting on continuous-time and discrete-time oscillators.
To develop a novel method for estimating the largest response Lyapunov exponent.

Main Methods:

Application of response (conditional) Lyapunov exponents to quantify synchronization robustness.
Development and demonstration of a new method for estimating the largest response Lyapunov exponent.
Utilizing twin response subsystems with master-slave coupling for exponent estimation.
Comparison with classical algorithms for Lyapunov exponent calculation.

Main Results:

A novel, effective method for estimating the largest response Lyapunov exponent is presented.
The method's application and comparison with classical algorithms are demonstrated.
The concept of effective response Lyapunov exponents is introduced for slightly different oscillators.

Conclusions:

The proposed method offers a robust way to estimate Lyapunov exponents for synchronization analysis.
This research advances the understanding and quantification of synchronization in complex systems.
The introduced effective response Lyapunov exponents provide a tool for assessing synchronizability in diverse oscillator arrays.