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Measuring interdependences in dissipative dynamical systems with estimated Fokker-Planck coefficients
Jens Prusseit1, Klaus Lehnertz
1Department of Epileptology, Neurophysics Group, University of Bonn, Sigmund-Freud-Strasse 25, Bonn, Germany. jprusseit@gmx.de
Summary
We developed a simple, automated method to quantify asymmetric coupling between noisy dynamical systems. This approach distinguishes deterministic and stochastic influences, applicable to model systems and epilepsy patient data.
Area of Science:
- Dynamical Systems Theory
- Nonlinear Dynamics
- Computational Neuroscience
Background:
- Understanding interdependences in complex systems is crucial.
- Dissipative systems with noise present unique challenges for analyzing coupling.
- Existing methods for quantifying coupling asymmetry are often computationally intensive or lack automation.
Purpose of the Study:
- To develop a data-driven approach for measuring interdependences between dissipative dynamical systems influenced by noise.
- To quantify the asymmetry in coupling in an automated, computationally inexpensive, and simple manner.
- To differentiate between interdependences in the deterministic and stochastic components of system dynamics.
Main Methods:
- Estimation of drift and diffusion coefficients from time series data.
- Utilizing a Fokker-Planck equation framework.
- Derivation of novel measures for quantifying coupling asymmetry.
Main Results:
- Successfully quantified asymmetric coupling in simulated time series from coupled stochastic and deterministic systems.
- Demonstrated the ability to distinguish between deterministic and stochastic influences on system coupling.
- Applied the method to electroencephalographic (EEG) recordings from epilepsy patients, revealing insights into neural interdependencies.
Conclusions:
- The proposed data-driven method provides an efficient and automated way to measure coupling asymmetry in noisy dynamical systems.
- This approach enhances the understanding of complex system interactions by separating deterministic and stochastic contributions.
- The application to epilepsy EEG data highlights its potential for analyzing neural dynamics and identifying pathological coupling patterns.
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