Nonlinear dynamical systems with control parameters may not be well modeled by shallow
neural networks. In this paper, the stable fixed-point solutions, periodic and chaotic solutions …

Abstract Echo State Network (ESN) is an effective variant of Recurrent Neural Network
(RNN). However, it is difficult for traditional ESN to determine the reservoir size that matches …

Chaos recognition is necessary to determine the prediction possibility for specific time
series. In this paper, we attempt to seek a novel chaos recognition method based on the …

We tackle the outstanding issue of analyzing the inner workings of neural networks trained
to classify regular-vs-chaotic time series. This setting, well-studied in dynamical systems …

A recent deterministic learning theory has achieved locally-accurate identification of
unknown system dynamics. This article presents a novel application of deterministic learning …

This paper studies the classification of large-scale time series data constructed by nonlinear
dynamical systems via deterministic learning. Firstly, a large-scale time series dataset …

This study performed a deep learning-based classification of chaotic systems over their
phase portraits. To the best of the authors' knowledge, such classification studies over phase …

The ability to uncover characteristics based on empirical measurement is an important step
in understanding the underlying system that gives rise to an observed time series. This is …

In recent years, the use of variable-order differential operators has emerged as a powerful
tool in the analysis of nonlinear fractional differential equations and chaotic systems. In …

To improve the security of chaotic image encryption algorithm, this paper proposes an image
encryption algorithm based on GRU (Gated Recurrent Unit) prediction to generate chaotic …