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Order parameter for the transition from strong to weak generalized synchrony from empirical mode decomposition
Kaustubh Manchanda1, Ramakrishna Ramaswamy
1School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
We introduce a new method using empirical mode decomposition to analyze chaotic time series in driven nonlinear systems. This technique identifies order parameters to distinguish between strong and weak generalized synchronization regimes.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Time Series Analysis
Background:
- Driven nonlinear dynamical systems can exhibit complex synchronization behaviors.
- Generalized synchronization is a key phenomenon in coupled chaotic systems.
- Distinguishing between strong and weak synchronization regimes is crucial for understanding system dynamics.
Purpose of the Study:
- To develop a novel method for characterizing generalized synchronization in driven nonlinear systems.
- To identify reliable order parameters for detecting transitions between synchronization states.
- To apply the developed method to various chaotic flows and maps.
Main Methods:
- Empirical Mode Decomposition (EMD) of chaotic time series.
- Analysis of instantaneous intrinsic mode frequencies and their variance.
- Application to chaotically driven flows and maps.
Main Results:
- Instantaneous intrinsic mode frequencies serve as effective order parameters.
- EMD successfully detects transitions between strong and weak generalized synchrony.
- The method is validated across diverse nonlinear systems.
Conclusions:
- Empirical Mode Decomposition offers a robust approach to quantify synchronization in chaotic systems.
- Instantaneous frequencies provide valuable insights into the dynamics of generalized synchronization.
- This work advances the understanding and detection of synchronization transitions.
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