Related Experiment Video
Updated: Aug 4, 2025
19:44
A Tactile Automated Passive-Finger Stimulator TAPS
Published on: June 3, 2009
13.8K
Stickiness and recurrence plots: An entropy-based approach.
Matheus R Sales1, Michele Mugnaine2, José D Szezech1
1Graduate Program in Sciences/Physics, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil.
Chaos (Woodbury, N.Y.)
|April 1, 2023
Summary
We introduce recurrence time entropy (RTE) to analyze quasi-integrable Hamiltonian systems. This new method reveals distinct dynamical behaviors in regular and chaotic regions, correlating with system complexity.
Area of Science:
- Nonlinear dynamics
- Statistical mechanics
- Chaos theory
Background:
- The stickiness effect is a key characteristic of quasi-integrable Hamiltonian systems.
- Understanding the interplay between regular and chaotic dynamics is crucial in these systems.
Purpose of the Study:
- To propose and validate a novel entropy-based measure for characterizing dynamics in quasi-integrable Hamiltonian systems.
- To investigate the relationship between recurrence time entropy and other measures of chaos.
Main Methods:
- Utilizing recurrence plots (RPs) to analyze system dynamics.
- Calculating recurrence time entropy (RTE) from the distribution of recurrence times in RPs.
- Comparing RTE with the largest Lyapunov exponent.
Main Results:
- Recurrence time entropy (RTE) shows a positive correlation with the largest Lyapunov exponent.
- Finite-time RTE exhibits a multi-modal distribution.
- Each mode in the RTE distribution corresponds to motion around hierarchical islands.
Conclusions:
- Recurrence time entropy is an effective measure for characterizing complex dynamics in quasi-integrable Hamiltonian systems.
- RTE successfully distinguishes between regular and chaotic regions and hierarchical structures.
Related Concept Videos
01:20Entropy and the Second Law of Thermodynamics
2.9K
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
2.9K
01:10Entropy Change in Reversible Processes
2.6K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.6K
01:17Probability Histograms
11.8K
A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
11.8K
01:07Residual Plots
4.9K
A residual plot is a statistical representation of data used to analyze correlation and regression results. It helps verify the requirements for drawing specific conclusions about correlation and regression. To obtain the residual plot, first, the residual for each data value is calculated, which is simply the vertical distance between the observed and the predicted value obtained from the regression equation.
When the residual values are plotted against the variable x, it is called a residual...
When the residual values are plotted against the variable x, it is called a residual...
4.9K
01:22Entropy within the Cell
10.9K
A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...
10.9K
01:14Relative Frequency Histogram
5.6K
The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. Like the histogram, a relative frequency histogram also has the same shape with a horizontal scale (the x-axis), but the vertical scale (the y-axis) is marked with relative frequencies (percentages of the whole) instead of actual frequencies. A relative frequency histogram is a graphical representation of a frequency distribution where the...
5.6K