Deep Learning Based Classification of Time Series of Chaotic Systems over Graphic Images

In this study, for the first time in the literature, identification of different chaotic systems by classifying graphic images of their time series with deep learning methods is aimed. For this purpose, a data set is generated that consists of the graphic images of time series of the most known three chaotic systems: Lorenz, Chen, and Rossler systems. The time series are obtained for different parameter values, initial conditions, step size and time lengths. After generating the data set, a high-accuracy classification is performed by using transfer learning method. In the study, the most accepted deep learning models of the transfer learning methods are employed. These models are SqueezeNet, VGG-19, AlexNet, ResNet50, ResNet101, DenseNet201, ShuffleNet and GoogLeNet. As a result of the study, classification accuracy is found between 96% and 97% depending on the problem. Thus, this study makes association of real time random signals with a mathematical system possible.

FPGA Realization and Lyapunov–Krasovskii Analysis for a Master-Slave Synchronization Scheme Involving Chaotic Systems and Time-Delay Neural Networks

In this paper, the trajectory tracking control and the field programmable gate array (FPGA) implementation between a recurrent neural network with time delay and a chaotic system are presented. The tracking error is globally asymptotically stabilized by means of a control law generated from the Lyapunov–Krasovskii and Lur’e theory. The applicability of the approach is illustrated by considering two different chaotic systems: Liu chaotic system and Genesio–Tesi chaotic system. The numerical results have shown the effectiveness of obtained theoretical results. Finally, the theoretical results are implemented on an FPGA, confirming the feasibility of the synchronization scheme and showing that it is hardware realizable.

A Modified Multivariable Complexity Measure Algorithm and Its Application for Identifying Mental Arithmetic Task

Properly measuring the complexity of time series is an important issue. The permutation entropy (PE) is a widely used as an effective complexity measurement algorithm, but it is not suitable for the complexity description of multi-dimensional data. In this paper, in order to better measure the complexity of multi-dimensional time series, we proposed a modified multivariable PE (MMPE) algorithm with principal component analysis (PCA) dimensionality reduction, which is a new multi-dimensional time series complexity measurement algorithm. The analysis results of different chaotic systems verify that MMPE is effective. Moreover, we applied it to the comlexity analysis of EEG data. It shows that the person during mental arithmetic task has higher complexity comparing with the state before mental arithmetic task. In addition, we also discussed the necessity of the PCA dimensionality reduction.

Finite-Time Synchronization Between Two Different Chaotic Systems by Adaptive Sliding Mode Control

The finite-time chaos synchronization between two different chaotic systems with uncertain parameters and external disturbances is studied. A new and improved adaptive fast nonsingular terminal sliding mode control (ANFTSM) has been designed for a fast rate convergence of tracking error to zero in finite time. The effectiveness of the proposed control method is shown in simulation results.

A New Hyperchaotic Map for a Secure Communication Scheme with an Experimental Realization

Using different chaotic systems in secure communication, nonlinear control, and many other applications has revealed that these systems have several drawbacks in different aspects. This can cause unfavorable effects to chaos-based applications. Therefore, presenting a chaotic map with complex behaviors is considered important. In this paper, we introduce a new 2D chaotic map, namely, the 2D infinite-collapse-Sine model (2D-ICSM). Various metrics including Lyapunov exponents and bifurcation diagrams are used to demonstrate the complex dynamics and robust hyperchaotic behavior of the 2D-ICSM. Furthermore, the cross-correlation coefficient, phase space diagram, and Sample Entropy algorithm prove that the 2D-ICSM has a high sensitivity to initial values and parameters, extreme complexity performance, and a much larger hyperchaotic range than existing maps. To empirically verify the efficiency and simplicity of the 2D-ICSM in practical applications, we propose a symmetric secure communication system using the 2D-ICSM. Experimental results are presented to demonstrate the validity of the proposed system.