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A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
Published on: May 25, 2019
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Review of sample-based methods used in an analysis of multistable dynamical systems
Maciej Leszczyński1, Przemysław Perlikowski1, Tomasz Burzyński1
1Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland.
Chaos (Woodbury, N.Y.)
|September 1, 2022
Summary
Analyzing multi-stable systems requires advanced techniques beyond classical methods. This study details sample-based methods like basin stability and basin entropy for understanding complex dynamics, aiding in selecting optimal analytical approaches.
Area of Science:
- Complex Systems Analysis
- Nonlinear Dynamics
- Computational Science
Background:
- Classical methods (bifurcation diagrams, Lyapunov exponents) struggle with multi-stable systems exhibiting numerous coexisting attractors.
- Understanding the global behavior of such complex systems necessitates alternative analytical strategies.
Purpose of the Study:
- To systematically review and compare various sample-based methods for analyzing multi-stable dynamical systems.
- To evaluate the advantages and disadvantages of these methods using a nonlinear oscillator model with multiple coexisting attractors.
Main Methods:
- Exploration of sample-based methods including basin stability, extended basin stability, constrained basin stability, basin entropy, time dependent stability margin, and survivability.
- Application and comparative analysis of these methods on an archetypal nonlinear oscillator system.
Main Results:
- Each sample-based method offers unique insights into system dynamics but none provides a complete picture.
- A combination of multiple sample-based methods is often required for a comprehensive understanding of complex system behavior.
Conclusions:
- Sample-based methods are crucial for analyzing multi-stable systems where classical approaches fail.
- This study provides guidance for researchers in selecting appropriate sample-based methods for dynamical system analysis.
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