Related Experiment Video
Updated: Jun 16, 2025
06:55
Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
Published on: August 5, 2016
8.2K
Basin stability for updating system uncertainties
Dawid Dudkowski1, Tomasz Kapitaniak1
1Division of Dynamics, <a href="https://ror.org/00s8fpf52">Lodz University of Technology</a>, Stefanowskiego 1/15, 90-537 Lodz, Poland.
Physical Review. E
|August 20, 2024
Summary
This study introduces a basin stability tool to update system properties under uncertainty. It uses Bayesian inference on coupled pendula to probabilistically refine knowledge of complex dynamical systems.
Area of Science:
- Physics
- Dynamical Systems Theory
- Complex Systems
Background:
- Complex dynamical systems often exhibit multiple coexisting behaviors (attractors).
- Parameter uncertainties in these systems complicate the analysis of their stability and behavior.
- Basin stability analysis quantifies the robustness of different system behaviors.
Purpose of the Study:
- To develop and apply a basin stability framework for updating system property knowledge under parameter uncertainty.
- To integrate basin stability mapping with Bayesian inference for probabilistic characterization of complex systems.
- To investigate the impact of parameter variations on basin stability calculations, especially near existence borders.
Main Methods:
- Utilized a classical mechanical model of coupled pendula exchanging energy through a supporting structure.
- Calculated basin stability maps for distinct dynamical behaviors (synchronous patterns, desynchronization).
- Employed Bayesian inference to combine prior parameter distributions with attractor occurrence data.
Main Results:
- Demonstrated how basin stability maps, when combined with Bayesian inference, yield updated posterior probability distributions for system properties.
- Showcased that attractor occurrence data refines knowledge of system parameters probabilistically.
- Highlighted significant differences in basin stability estimation when parameter variations are considered versus fixed parameters, particularly near behavior existence borders.
Conclusions:
- The proposed application of basin stability analysis offers a probabilistic approach to studying complex dynamical systems.
- This method enhances understanding of system properties by updating information under parameter uncertainties.
- Careful consideration of estimation methods, especially near existence borders, is crucial for reliable applications.
Related Concept Videos
01:24Pole and System Stability
264
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
264
01:10Propagation of Uncertainty from Systematic Error
491
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
491
00:59Propagation of Uncertainty from Random Error
658
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
658
01:25Multimachine Stability
150
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
150
01:13Stability of Equilibrium Configuration: Problem Solving
602
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Problem-solving in the context of the stability of equilibrium configuration...
602
01:23Stability of Equilibrium Configuration
442
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
442