Recent developments in engineering applications of stochastic resonance have expanded to various fields, especially biomedicine. Deterministic chaos generates a phenomenon known as chaotic resonance, which is similar to stochastic resonance. However, engineering applications of chaotic resonance are limited owing to the problems in controlling chaos, despite its uniquely high sensitivity to weak signal responses. To tackle these problems, a previous study proposed “reduced region of orbit” (RRO) feedback methods, which cause chaotic resonance using external feedback signals. However, this evaluation was conducted under noise-free conditions. In actual environments, background noise and measurement errors are inevitable in the estimation of RRO feedback strength; therefore, their impact must be elucidated for the application of RRO feedback methods. In this study, we evaluated the chaotic resonance induced by the RRO feedback method in chaotic neural systems in the presence of stochastic noise. Specifically, we focused on the chaotic resonance induced by RRO feedback signals in a neural system composed of excitatory and inhibitory neurons, a typical neural system wherein chaotic resonance is observed in the presence of additive noise and feedback signals including the measurement error (called contaminant noise). It was found that for a relatively small noise strength, both types of noise commonly degenerated the degree of synchronization in chaotic resonance induced by RRO feedback signals, although these characteristics were significantly different. In contrast, chaos-chaos intermittency synchronization was observed for a relatively high noise strength owing to the noise-induced attractor merging bifurcation for both types of noise. In practical neural systems, the influence of noise is unavoidable; therefore, this study highlighted the importance of the countermeasures for noise in the application of chaotic resonance and utilization of noise-induced attractor merging bifurcation.

In this letter, we will prove that chaotic binary sequences generated by the tent map and Walsh functions are i.i.d. (independent and identically distributed) and orthogonal to each other.

Fluctuations in nonlinear systems can enhance the synchronization with weak input signals. These nonlinear synchronization phenomena are classified as stochastic resonance and chaotic resonance. Many applications of stochastic resonance have been realized, utilizing its enhancing effect for the signal sensitivity. However, although some studies showed that the sensitivity of chaotic resonance is higher than that of stochastic resonance, only few studies have investigated the engineering application of chaotic resonance. A possible reason is that, in chaotic resonance, the chaotic state must be adjusted through internal parameters to reach the state that allows resonance. In many cases and especially in biological systems, such adjustments are difficult to perform externally. To overcome this difficulty, we developed a method to control the chaotic state for an appropriate state of chaotic resonance by using an external feedback signal. The method is called reducing the range of orbit (RRO) feedback method. Previously, we have developed the RRO feedback method for discrete chaotic systems. However, for applying the RRO feedback method to actual chaotic systems including biological systems, development of the RRO feedback signals in continuous chaotic systems must be considered. Therefore, in this study, we extended the RRO feedback method to continuous chaotic systems by focusing on the map function on the Poincaré section. We applied the extended RRO feedback method to Chua's circuit as a continuous chaotic system. The results confirmed that the RRO feedback signal can induce chaotic resonance. This study is the first to report the application of RRO feedback to a continuous chaotic system. The results of this study will facilitate further device development based on chaotic resonance.

This paper presents an analysis of random number generators based on continuous-time chaotic oscillators. Two different methods for random number generation have been studied: 1) Regular sampling of a chaotic waveform, and 2) Chaotic sampling of a regular waveform. Kernel density estimation is used to analytically describe the distribution of chaotic state variables and the probability density function corresponding to the output bit stream. Random bit sequences are generated using analytical equations and results from numerical simulations. Applying the concepts of autocorrelation and approximate entropy, randomness quality of the generated bit sequences are assessed to analyze relationships between the frequencies of the regular and chaotic waveforms used in both random number generation methods. It is demonstrated that in both methods, there exists certain ratios between the frequencies of regular and chaotic signal at which the randomness of the output bit stream changes abruptly. Furthermore, both random number generation methods have been compared against their immunity to interference from external signals. Analysis shows that chaotic sampling of regular waveform method provides more robustness against interference compared to regular sampling of chaotic waveform method.

This paper concerned the research on a memristive chaotic system and the generated random sequence; by constructing a piecewise-linear memristor model, a kind of chaotic system is constructed, and corresponding numerical simulation and dynamical analysis are carried out to show the dynamics of the new memristive chaotic system. Finally the proposed memristive chaotic system is used to generate random sequence for the possible application in encryption field.

Stochastic resonance (SR) is a phenomenon in which signal response in a nonlinear system is enhanced by noise. Fluctuating activities in deterministic chaos are known to cause a phenomenon called chaotic resonance (CR), which is similar to SR. Most previous studies on CR showed that these signal responses were controlled by internal parameters. However, in several applications of CR, it is difficult to control these parameters externally, particularly in biological systems. In this study, to overcome this difficulty, we propose a method for controlling the signal response of CR by adjusting the strength of external feedback control. By using this method, we demonstrate the control of CR in a one-dimensional cubic map, where CR arises from chaos-chaos switching to a weak input signal.

This letter proposes a numerical method for approximating the location of and dynamics on a class of chaotic saddles. In contrast to the conventional strategy of maximizing the escape time, our proposal is to impose a zero-expansion condition along transversely repelling directions of chaotic saddles. This strategy exploits the existence of skeleton-forming unstable periodic orbits embedded in chaotic saddles, and thus can be conveniently implemented as a variant of subspace Newton-type methods. The algorithm is examined through an illustrative and another standard example.

In this paper, we introduce a self-constructive Normalized Gaussian Network (NGnet) for online learning tasks. In online tasks, data samples are received sequentially, and domain knowledge is often limited. Then, we need to employ learning methods to the NGnet that possess robust performance and dynamically select an accurate model size. We revise a previously proposed localized forgetting approach for the NGnet and adapt some unit manipulation mechanisms to it for dynamic model selection. The mechanisms are improved for more robustness in negative interference prone environments, and a new merge manipulation is considered to deal with model redundancies. The effectiveness of the proposed method is compared with the previous localized forgetting approach and an established learning method for the NGnet. Several experiments are conducted for a function approximation and chaotic time series forecasting task. The proposed approach possesses robust and favorable performance in different learning situations over all testbeds.

This paper considers the behavior of a master-slave system of two coupled piecewise constant spiking oscillators (PWCSOs). The master of this system exhibits chaos and outputs a chaotic sequence of spikes, which are used as input to the slave. The slave exhibits a periodic-like trajectory (PLT) that is chaotic but that appears to be periodic in the phase plane. We theoretically investigate the generating region of the PLT in the parameter space. Using a test circuit, we confirm the typical phenomena of this coupled system.

This paper deals with the security of chaos-based “true” random number generators (RNG)s. An attack method is proposed to analyze the security weaknesses of chaos-based RNGs and its convergence is proved using a master slave synchronization scheme. Attack on a RNG based on a double-scroll attractor is also presented as an example. All secret parameters of the RNG are revealed where the only information available is the structure of the RNG and a scalar time series observed from the double-scroll attractor. Simulation and numerical results of the proposed attack method are given such that the RNG doesn't fulfill NIST-800-22 statistical test suite, not only the next bit but also the same output bit stream of the RNG can be reproduced.

In this paper, synchronization for uncertain fractional order chaotic systems is investigated. By using the fractional order extension of the Lyapunov stability criterion, a linear feedback controller and an adaptive controller are designed for synchronizing uncertain fractional order chaotic systems without and with unknown external disturbance, respectively. Quadratic Lyapunov functions are used in the stability analysis of fractional-order systems, and fractional order adaptation law is constructed to update design parameter. The proposed methods can guarantee that the synchronization error converges to zero asymptotically. Finally, illustrative examples are given to confirm the theoretical results.

To ensure the security of image transmission, this paper presents a new image encryption algorithm based on a genetic algorithm (GA) and a piecewise linear chaotic map (PWLCM), which adopts the classical diffusion-substitution architecture. The GA is used to identify and output the optimal encrypted image that has the highest entropy value, the lowest correlation coefficient among adjacent pixels and the strongest ability to resist differential attack. The PWLCM is used to scramble pixel positions and change pixel values. Experiments and analyses show that the new algorithm possesses a large key space and resists brute-force, statistical and differential attacks. Meanwhile, the comparative analysis also indicates the superiority of our proposed algorithm over a similar, recently published, algorithm.

Since substitution boxes (S-boxes) are the only nonlinear portion of most block ciphers, the design of cryptographically strong and low-complexity S-boxes is of great importance in cryptosystems. In this paper, a new kind of S-boxes obtained by iterating a discretized piecewise linear map is proposed. The S-box has an implementation efficiency both in software and hardware. Moreover, the results of performance test show that the proposed S-box has good cryptographic properties.

This paper presents an implementation of a digital chaotic signal generator based on compound one-dimensional sinusoidal maps. The proposed chaotic map not only offers high chaoticity measured from a positive lyapunov exponent but also provides diverse bifurcation structures with robust chaos over most regions of parameter spaces. Implementation on FPGA realizes small number of components and offers a highly random chaotic sequence with no autocorrelation. The proposed chaotic signal generator offers a potential alternative in random test pattern generation or in secured data communication applications.

This paper proposes the synchronization control method for two different unified chaotic systems with unknown mismatched parameters using sum of squares method. Previously, feedback-linearizing and stabilization terms were used in the controller for the synchronization problem. However, they used just a constant matrix as a stabilization control gain, whose performance is shown to be valid only for a linear model. Thus, we propose the novel control method for the synchronization of the two different unified chaotic systems with unknown mismatched parameters via sum of squares method. We design the stabilization control input which is of the polynomial form by sum of squares method and also the adaptive law for the estimation of the unknown mismatched parameter between the master and slave systems. Since we can use the polynomial control input which is dependent on the system states as the stabilization controller, the proposed method can have better performance than the previous methods. Numerical simulations for both uni-directional and bi-directional chaotic systems show the validity and advantage of the proposed method.

A new training algorithm for the chaotic Adachi Neural Network (AdNN) is investigated. The classical training algorithm for the AdNN and it's variants is usually a “one-shot” learning, for example, the Outer Product Rule (OPR) is the most used. Although the OPR is effective for conventional neural networks, its effectiveness and adequateness for Chaotic Neural Networks (CNNs) have not been discussed formally. As a complementary and tentative work in this field, we modified the AdNN's weights by enforcing an unsupervised Hebbian rule. Experimental analysis shows that the new weighted AdNN yields even stronger dynamical associative memory and pattern recognition phenomena for different settings than the primitive AdNN.

This paper clarifies the bifurcation structure of the chaotic attractor in an interrupted circuit with switching delay from theoretical and experimental view points. First, we introduce the circuit model and its dynamics. Next, we define the return map in order to investigate the bifurcation structure of the chaotic attractor. Finally, we discuss the dynamical effect of switching delay in the existence region of the chaotic attractor compared with that of a circuit with ideal switching.

In 2010, Guo and Zhang proposed a group key agreement protocol based on the chaotic hash function. This letter points out that Guo-Zhang's protocol is still vulnerable to off-line password guessing attacks, stolen-verifier attacks and reflection attacks.

A novel random number generation method based on chaotic sampling of regular waveform is proposed. A high speed IC truly random number generator based on this method is also presented. Simulation and experimental results, verifying the feasibility of the circuit, are given. Numerical binary data obtained according to the proposed method pass the four basic tests of FIPS-140-2, while experimental data pass the full NIST-800-22 random number test suite without post-processing.

The code division multiplexing (CDM)-based MIMO channel sounder architecture is efficient at measuring fast fading MIMO channels. This paper examines loosely synchronous (LS), CAZAC, Kasami, and Chaotic sequences as probing signals in the CDM architecture. After comparing the performance of the channel measurement among the sequences, it is concluded that the LS sequences are the most appropriate codes for the probing signals. However, because LS sequences have a significant drawback in that the number of transmit antennas is limited to less than 4, we propose using a hybrid architecture combining CDM with TDM for supporting a greater number of transmit antennas. The simulation results show that the proposed scheme can improve the measurement performance when more than 4 transmit antennas are used.