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Basin entropy: a new tool to analyze uncertainty in dynamical systems
Alvar Daza1, Alexandre Wagemakers1, Bertrand Georgeot2
1Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Móstoles, Madrid, Tulipán s/n, 28933, Spain.
Scientific Reports
|August 13, 2016
Summary
We introduce basin entropy, a new measure to quantify uncertainty in predicting system outcomes. This helps understand complex systems in fields like neuroscience and economics, identifying when outcomes are unpredictable.
Area of Science:
- Nonlinear dynamics
- Complex systems analysis
- Predictive modeling
Background:
- Basins of attraction map initial conditions to final states in dynamical systems.
- Predicting final states can be challenging due to the complex nature of these basins.
- Uncertainty quantification is crucial across diverse scientific disciplines.
Purpose of the Study:
- To introduce a novel quantitative measure for unpredictability in dynamical systems.
- To provide a tool for analyzing systems with multiple possible outcomes.
- To establish a criterion for identifying fractal basin boundaries.
Main Methods:
- Development of the basin entropy metric.
- Application to paradigmatic examples in nonlinear dynamics.
- Analysis of system behavior across varying parameters.
Main Results:
- Basin entropy quantifies the uncertainty in predicting final states.
- Identified key factors contributing to prediction difficulty.
- Established a condition (basin entropy > log2) for fractal basin boundaries.
Conclusions:
- Basin entropy offers an efficient method to probe system dynamics and uncertainty.
- The new metric aids in understanding and classifying unpredictability.
- Provides a clear criterion for detecting fractal basin boundaries, enhancing dynamical system analysis.
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