Search the site for the term 'chaotic dynamics'

In some other articles in this blog, I have already written about complex time series, recurrence quantification analysis (RQA) and neural networks. In this series of articles, I will discuss some points to take into account when combining the use of these two tools to identify patterns in complex series, such as detecting anomalies in electrocardiograms or electroencephalograms.

[Read More...]

This is the last article of the series dedicated to the WinCA application. This application allows the edition and to execution of cellular automata. To finish, I will review the code that implements the automaton itself, using all the classes and interfaces explained in the previous articles.

[Read More...]

I continue explaining the basics of the WinCA application code, dedicated to the designing and execution of cellular automata. This time I will tell you about the implementation of the cells and other auxiliary classes needed to build and execute automata.

[Read More...]

We continue with the series dedicated to cellular automata and the WinCA application, dedicated to build and executing them. In this article I will explain the code related to the expression system that allows establishing the conditions to change from one state to another.

[Read More...]

I continue to comment on the source code of the WinCA program, dedicated to cellular automata. In this article I will explain the interfaces and classes with which cell states are implemented and their edition. You can use these interfaces and classes as a basis to extend the application features.

[Read More...]

Once reviewed the operation of the WinCA application, dedicated to cellular automata, let's see how the source code is organized. In this article I will explain the properties of cell states, and how they can be extended to add new functionalities by implementing new classes with the corresponding interfaces.

[Read More...]

In this article, third of the series, I continue to explain the operation of the WinCA application, devoted to the construction and execution of cellular automata. This time I will show the language used to define the transitions between the different states of the automaton cells.

[Read More...]

This is the second article in the series about the WinCA application, dedicated to the construction and execution of cellular automata. In this article I will show how to design the diferent states that can have the automaton cells, and the properties that can be assigned to them, using the application editors.

[Read More...]

Cellular automata are mathematical models used to study the evolution of complex dynamic systems by simulating the interactions over time of a large number of elements, called cells. In this series of articles I will present the WinCA application, with which you can build and run this type of objects.

[Read More...]

WInRQA is an application dedicated to recurrence plots, a tool that is used in the analysis of recurrence of complex time series. In this article I will introduce a new tool that I have added to the program. Until now, the measures of quantification of recurrence (RQM) were obtained only from a static portion of the original series. With the new tool, we can obtain a series of measures by moving a window along the entire original series and calculating the corresponding measurements to each of these windows.

[Read More...]

The Iterated function systems (IFS) are a simple mathematical tool for constructing fractal sets through a series of contractive affine applications. This method was developed by M.F. Barnsley in 1985. In particular, it is useful to obtain a self-similar fractal based on iteratively applying the system of functions to any set, until arriving at a good approximation of the fractal set that constitutes the attractor of the system.

[Read More...]

In this article I will show how, through a very simple and totally deterministic process, we can move from a stationary system to a completely random one, going through periodic and chaotic dynamics. For this, I will generate several time series with these characteristics using the program R and several packages that can help us in the analysis of them.

[Read More...]

To conclude this series on complex time series and their characterization using graphical tools I will show you a tool called recurrence plot, which allows to obtain some measures used in the recurrence quantification analysis, or RQA for its acronym in English. The recurrence is a characteristic property of deterministic dynamical systems, and consists of that two or more states of the system are arbitrarily close after a certain period of time.

[Read More...]

In this new article in the series on time series with complex dynamics, I will show you a procedure to approximately reconstruct the information of a dynamic system with two or more variables from a single series, i.e. a set of data in a single dimension. What we will get from this unique series is a new one for each of the extra dimensions with which we intend to extend the model.

[Read More...]

The recurrent neural networks are a very appropriate tool for modeling time series. This is a type of network architecture that implements some kind of memory and, therefore, a sense of time. This is achieved by implementing some neurons receiving as input the output of one of the hidden layers, and injecting their output again in that layer. In this article I will show a simple way to use two neural networks of this kind, the Elman and Jordan ones, using the program R.

[Read More...]

In this new article of the series dedicated to the graphic characterization of complex time series I will talk about two other graphical tools that can be useful, the power spectrum of the signal, which will be obtained through the Fourier transform, and the graph of the distribution of values of the series, a simple histogram with the frequency of the different values that also can provide us information about the series dynamics.

[Read More...]

In this new article in the series on graphic characterization of time series from dynamical systems with chaotic dynamics, I will talk about a way to represent such systems in the domain of space, independently of time, the phase diagram. With this type of diagram, you can see the attractors of the system. An attractor is a point, a curve, in general, a set of points to which converge the system equations, which gives us an idea of the typical behavior of that system.

[Read More...]

I continue the series on graphic characterization of the complexity in time series using the helper application GraphStudy. In this article I will show how to construct a graph with which you can easily distinguish whether a particular series from an iterated function presents a chaotic dynamics, the web diagram.

[Read More...]

Many of the data sets with which we usually work are in the form of time series. A time series can be seen as the evolution of a dynamic system, characterized by some variables and parameters. Depending on the type of dynamic of the system, the series may be stationary, periodic, quasiperiodic, chaotic or random. In this series of articles, I will focus on the characterization of chaotic dynamics, which is presented by complex systems, by using graphical methods.

[Read More...]