Strengthening Quality of Chaotic Bit Sequences

We discuss chaos and its quality as measured through the 0-1 test for chaos. When the 0-1 test indicates deteriorating quality of chaos, because of the finite precision representations of real numbers in digital implementations, then the process may eventually lead to a periodic sequence. A simple method for improving the quality of a chaotic signal is to mix the signal with another signal by using the XOR operation. In this paper, such mixing of weak chaotic signals is considered, yielding new signals with improved quality (with K values from the 0-1 test close to 1). In some sense, such a mixing of signals could be considered as a two-layer prevention strategy to maintain chaos. That fact may be important in those applications when the hardware resources are limited. The 0-1 test is used to show the improved chaotic behavior in the case when a continuous signal (for example, from the Chua, Rössler or Lorenz system) intermingles with a discrete signal (for example, from the logistic, Tinkerbell or Henon map). The analysis is presented for chaotic bit sequences. Our approach can further lead to hardware applications, and possibly, to improvements in the design of chaotic bit generators. Several illustrative examples are included.

Permutation Entropy of Weakly Noise-Affected Signals

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.

A Fast Method for Detecting Interdependence between Time Series and Its Directionality

We propose a fast nonlinear method for assessing quantitatively both the existence and directionality of linear and nonlinear couplings between a pair of time series. We test this method, called Boolean Slope Coherence (BSC), on bivariate time series generated by various models, and compare our results with those obtained from different well-known methods. A similar approach is employed to test the BSC’s capability to determine the prevalent coupling directionality. Our results show that the BSC method is successful for both quantifying the coupling level between a pair of signals and determining their directionality. Moreover, the BSC method also works for noisy as well as chaotic signals and, as an example of its application to real data, we tested it by analyzing neurophysiological recordings from visual cortices.

Chua’s Circuit Simulation Experiment Based on Saturation Function

This paper designs a Chua's diode circuit based on saturation function. It uses Matlab/Simulink to model Chua's circuit, and simulates and analyzes the dynamic behavior of chaos, the model simply generates efficient chaotic signals, and intuitively displays processes of the chaotic attractor, chaotic synchronization, period doubling and the road to chaos through the virtual oscilloscope, which is conducive to chaotic beginners' understanding of the basic characteristics and application of chaos. The electrical and mathematical analysis of the instrument is carried out by simulation, to explore the functions of each parameter, and helps beginners to understand its working principle more quickly and conduct experimental operations. It provides theoretical support for the improvement and optimization of Chua's circuit.

Multi-Scroll Attractors with Hyperchaotic Behavior Using Fractional-Order Systems

In this paper, a systematic design is proposed to generate multi-scroll attractors with hyperchaotic behavior using fractional-order systems, in which switched SC-CNN is triggered with error function. Sprott Systems Case H is reconstructed with fractional-order switched SC-CNN system. Herein, the goal is to increase the complexity of chaotic signals, hence providing safer and reliable communication by generating multi-scroll attractors with hyperchaotic behavior using fractional-order systems. Theoretical analysis of the proposed system’s dynamical behaviors is scrutinized, while numerical investigations are carried out with equilibrium points, Lyapunov exponent, bifurcation diagrams, Poincaré mapping and 0/1 test methods. Numerical results are validated through simulations and on an FPAA platform.

English Speech Feature Recognition Based On Digital Means

In order to improve the effect of English speech recognition, based on digital means, this paper combines the actual needs of English speech feature recognition to improve the digital algorithm. Moreover, this paper combines fuzzy recognition algorithm to analyze English speech features, and analyzes the shortcomings of traditional algorithms, and proposes the fuzzy digitized English speech recognition algorithm, and builds an English speech feature recognition model on this basis. In addition, this paper conducts time-frequency analysis on chaotic signals and speech signals, eliminates noise in English speech features, improves the recognition effect of English speech features, and builds an English speech feature recognition system based on digital means. Finally, this paper conducts grouping experiments by inputting students' English pronunciation forms, and counts the results of the experiments to test the performance of the system. The research results show that the method proposed in this paper has a certain effect.

Adaptive Control of Chaotic Signals: Investigated by Simulation Software and Real Electronic Circuits

Chaotic behavior is complicated, sensitive, and has the feature of great variety, which are the most potential signals to be applied in data encryption, secure communication, medical information protection, etc. As a consequence, in this paper, we try to propose three different ways to show our data generating results step by step, which means it can be proved effectively and used in practice: (1) Chaotic solutions simulated by MATLAB, (2) chaotic motion drawn via electronic circuits software Multisim, and (3) chaotic signal implemented on real electronic circuits with breadboard. In advance, following the same design principal, the adaptive chaotic signal is also designed and presented in the end of this article for further study, which provides a more flexible and variable chaotic signal to enhance the encryption effectiveness. The experimental results are extremely close to the two simulation results and can definitely be technically transferred to real encryption application.

Secure OFDM with Peak-to-Average Power Ratio Reduction Using the Spectral Phase of Chaotic Signals

In this paper, a new physical layer security technique is proposed for Orthogonal Frequency Division Multiplexing (OFDM) communication systems. The security is achieved by modifying the OFDM symbols using the phase information of chaos in the frequency spectrum. In addition, this scheme reduces the Peak to Average Power Ratio (PAPR), which is one of the major drawbacks of OFDM. The Selected Mapping (SLM) technique for PAPR reduction is employed to exploit the random characteristics of chaotic sequences. The reduction with this algorithm is shown to be similar to that of other SLM schemes, but it has lower computational complexity and side information does not have to be sent to the receiver. The security of this technique stems from the noise like behavior of chaotic sequences and their dependence on the initial conditions of the chaotic generator (which are used as the key). Even a slight difference in the initial conditions will result in a different phase sequence, which prevents an eavesdropper from recovering the transmitted OFDM symbols.

Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, $$\alpha$$ α , that determines the strength of the correlation of the noise. To predict $$\alpha$$ α the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the $$\alpha$$ α value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same $$\alpha$$ α parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community.