Classification of hyperchaotic, chaotic, and regular signals using single nonlinear node delay-based reservoir computers

Abstract

The Lyapunov exponent method is generally used for classifying hyperchaotic, chaotic, and regular dynamics based on the equations modeling the system. However, several systems do not benefit from appropriate modeling underlying their dynamic behaviors. Therefore, having methods for classifying hyperchaotic, chaotic, and regular dynamics using only the observational data generated either by the theoretical or the experimental systems is crucial. In this paper, we use single nonlinear node delay-based reservoir computers to separate hyperchaotic, chaotic, and regular dynamics. We show that their classification capabilities are robust with an accuracy of up to 99.61% and 99.03% using the Mackey–Glass and the optoelectronic oscillator delay-based reservoir computers, respectively. Moreover, we demonstrate that the reservoir computers trained with the two-dimensional Hénon-logistic map can classify the dynamical state of another system (for instance, the two-dimensional sine-logistic modulation map). Our solution extends the state-of-the-art machine learning and deep learning approaches for chaos detection by introducing the detection of hyperchaotic signals.