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Detecting determinism in high-dimensional chaotic systems
G J Ortega1, C Degli Esposti Boschi, E Louis
1Centro de Estudios e Investigaciones and Consejo Nacional de Investigaciones Cientificas y Técnicas, Universidad Nacional de Quilmes, R. S. Peña 180, 1876, Bernal, Argentina.
This study introduces a statistical method to detect determinism in complex, high-dimensional systems. The approach successfully distinguishes between deterministic and stochastic processes, even in systems with up to 13 dimensions.
Area of Science:
- Complex systems analysis
- Statistical physics
- Nonlinear dynamics
Background:
- Distinguishing deterministic from stochastic systems is crucial in many scientific fields.
- High-dimensional systems pose significant challenges for traditional analysis methods.
Purpose of the Study:
- To develop and validate a novel statistical method for identifying determinism in high-dimensional systems.
- To assess the method's efficacy in discriminating between stochastic and deterministic behaviors.
Main Methods:
- Statistical evaluation of the measure's differentiability along system trajectories.
- Application to simulated high-dimensional systems (up to dimension 13).
Main Results:
- The proposed method effectively discriminates between stochastic and deterministic systems.
- Successful identification of determinism in simulated high-dimensional systems.
- Demonstrated capability in analyzing simulated electroencephalogram (EEG) signals from high-dimensional deterministic sources.
Conclusions:
- The statistical differentiability method is a robust tool for detecting determinism in high-dimensional dynamics.
- This approach offers a promising avenue for analyzing complex real-world data, such as EEG signals.
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