A new computational approach to detecting chaos

Artist concept.

Chaos isn’t always bad for technology, in fact it can have several useful applications if it can be detected and identified.

Chaos and its chaotic dynamics are prevalent in nature and through manufactured devices and technology. Although chaos is generally seen as a negative, something to remove from systems to keep them running optimally, there are circumstances where chaos can be a benefit and may even have important applications. Hence a growing interest in the detection and classification of chaos in systems.

A new article published in EPJ B written by Dagobert Wenkack Liedji and Jimmi Hervé Talla Mbé from the Condensed Matter, Electronics and Signal Processing Research Unit, Department of Physics, University of Dschang, Cameroon, and Godpromesse Kenné, from the Laboratory of Automatic Control and Applied Computer Science, Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Cameroon proposes to use nonlinear node lag-based reservoir computer to identify chaotic dynamics.

In the paper, the authors show that the classification capabilities of this system are robust with a accuracy more than 99 percent. By examining the effect of time series length on method performance, they found greater accuracy achieved when the nonlinear single-node lag-based reservoir computer was used with short time series. chronological.

Several quantifiers have been developed to distinguish chaotic dynamics in the past, especially the largest Lyapunov exponent (LLE), which is very reliable and helps to display numerical values ​​that help decide the dynamical state of the system.

The team overcame LLE-related issues such as expense, the need for mathematical modeling of the system, and long processing times by studying several deep learning models, finding that these models achieved low classification rates. The exception to this was a large kernel size convolutional neural network (LKCNN) which could classify chaotic and non-chaotic time series with high accuracy.

Thus, using the Mackey-Glass (MG) delay-based reservoir computing system to classify non-chaotic and chaotic dynamical behaviors, the authors showed the ability of the system to act as an efficient and robust quantifier to classify non-chaotic signals. chaotic and chaotic.

They listed the advantages of the system they were using as not necessarily requiring knowledge of the set of equations, instead describing the dynamics of a system but only the data of the system, and the fact that the neuromorphic implementation Using an analog tank computer allows the real-time detection of the dynamic behaviors of a given oscillator.

The team concludes that future research will be devoted to deep reservoir computers to explore their performance in classifications of more complex dynamics.

Reference: “Chaos Recognition Using a Nonlinear Single-Node Delay-Based Reservoir Computer” by Dagobert Wenkack Liedji, Jimmi Hervé Talla Mbé, and Godpromesse Kenné, January 27, 2022, The European physical journal B.
DOI: 10.1140/epjb/s10051-022-00280-6

Sherry J. Basler