To address the challenge of target signals being completely submerged by ionospheric clutter during typhoon passages, this letter proposes a chaotic detection method for target signals in the background of ionospheric noise under typhoon excitation. Experimental results demonstrate the effectiveness of the proposed method in detecting target signals with harmonic characteristics from strong ionospheric clutter during typhoon passages.

Recent years have seen a general resurgence of interest in analog signal processing and computing architectures. In addition, extensive theoretical and experimental literature on chaos and analog chaotic oscillators exists. One peculiarity of these circuits is the ability to generate, despite their structural simplicity, complex spatiotemporal patterns when several of them are brought towards synchronization via coupling mechanisms. While by no means a systematic survey, this paper provides a personal perspective on this area. After briefly covering design aspects and the synchronization phenomena that can arise, a selection of results exemplifying potential applications is presented, including in robot control, distributed sensing, reservoir computing, and data augmentation. Despite their interesting properties, the industrial applications of these circuits remain largely to be realized, seemingly due to a variety of technical and organizational factors including a paucity of design and optimization techniques. Some reflections are given regarding this situation, the potential relevance to discontinuous innovation in analog circuit design of chaotic oscillators taken both individually and as synchronized networks, and the factors holding back the transition to higher levels of technology readiness.

In this paper, a circuit based on a field programmable analog array (FPAA) is proposed for three types of chaotic spiking oscillator (CSO). The input/output conversion characteristics of a specific element in the FPAA can be defined by the user. By selecting the proper characteristics, three types of CSO are realized without changing the structure of the circuit itself. Chaotic attractors are observed in a hardware experiment. It is confirmed that the dynamics of the CSOs are consistent with numerical simulations.

Today's electronic devices must meet many requirements, such as those related to performance, limits to the radiated electromagnetic field, size, etc. For such a design, the requirement is to have a solution that simultaneously meets multiple objectives that sometimes include conflicting requirements. In addition, it is also necessary to consider uncertain parameters. This paper proposes a new combination of statistical analysis using the Polynomial Chaos (PC) method for dealing with the random and multi-objective satisfactory design using the Preference Set-based Design (PSD) method. The application in this paper is an Electromagnetic Interference (EMI) filter for a practical case, which includes plural element parameters and uncertain parameters, which are resistors at the source and load, and the performances of the attenuation characteristics. The PC method generates simulation data with high enough accuracy and good computational efficiency, and these data are used as initial data for the meta-modeling of the PSD method. The design parameters of the EMI filter, which satisfy required performances, are obtained in a range by the PSD method. The authors demonstrate the validity of the proposed method. The results show that applying a multi-objective design method using PSD with a statistical method using PC to handle the uncertain problem can be applied to electromagnetic designs to reduce the time and cost of product development.

In recent years, physical layer security (PLS), which utilizes the inherent randomness of wireless signals to perform encryption at the physical layer, has attracted attention. We propose chaos modulation as a PLS technique. In addition, a method for encryption using a special encoder of polar codes has been proposed (PLS-polar), in which PLS can be easily achieved by encrypting the frozen bits of a polar code. Previously, we proposed a chaos-modulated polar code transmission method that can achieve high-quality and improved-security transmission using frozen bit encryption in polar codes. However, in principle, chaos modulation requires maximum likelihood sequence estimation (MLSE) for demodulation, and a large number of candidates for MLSE causes characteristic degradation in the low signal-to-noise ratio region in chaos polar transmission. To address this problem, in this study, we propose a versatile frozen bit method for polar codes, in which the frozen bits are also used to reduce the number of MLSE candidates for chaos demodulation. The numerical results show that the proposed method shows a performance improvement by 1.7dB at a block error rate of 10-3 with a code length of 512 and a code rate of 0.25 compared with that of conventional methods. We also show that the complexity of demodulation can be reduced to 1/16 of that of the conventional method without degrading computational security. Furthermore, we clarified the effective region of the proposed method when the code length and code rate were varied.

With the recent commercialization of fifth-generation mobile communication systems (5G), wireless communications are being used in various fields. Accordingly, the number of situations in which sensitive information, such as personal data is handled in wireless communications is increasing, and so is the demand for confidentiality. To meet this demand, we proposed a chaos-based radio-encryption modulation that combines physical layer confidentiality and channel coding effects, and we have demonstrated its effectiveness through computer simulations. However, there are no demonstrations of performances using real signals. In this study, we constructed a transmission system using Universal Software Radio Peripheral, a type of software-defined radio, and its control software LabVIEW. We conducted wired transmission experiments for the practical use of radio-frequency encrypted modulation. The results showed that a gain of 0.45dB at a bit error rate of 10-3 was obtained for binary phase-shift keying, which has the same transmission efficiency as the proposed method under an additive white Gaussian noise channel. Similarly, a gain of 10dB was obtained under fading conditions. We also evaluated the security ability and demonstrated that chaos modulation has both information-theoretic security and computational security.

We achieved detailed characterization of resonant tunneling chaos generator circuits in microwave frequency range. The circuit is analogous to Duffing oscillator, where the third-order nonlinear potential term is emulated by the nonlinear current-voltage curve of the resonant tunneling diode. The circuit includes a periodic reset mechanism to output identical chaos signal, which is essential to observe chaos signal on a sampling oscilloscope. Though this was shown to be effective in our previous papers, the length of the waveforms to observe is limited to rather short period, and it was unclear if this technique can be used for detailed characterization of such high-frequency chaos. In this paper, we improved the circuit design to observe longer waveforms, and demonstrated that the detailed characterization is possible using this periodic resetting technique with a sampling oscilloscope. The hybrid integration scheme is also used in this paper, which allows the easiest and shortest way to mimic a circuit as per circuit design, and precise estimation of circuit parameters aiming to eliminate circuit-related abnormalities. We provide deep insight into the dynamics associated with our circuit, starting from the single period, double period, chaos, and triple period regimes, by extracting power spectra, return maps, phase portraits, and bifurcation diagrams from acquired time series using sampling oscilloscope. Our method to study microwave chaotic signals can be applied to much higher frequency ranges, such as THz frequency range.

In recent years, physical layer security (PLS), which is based on information theory and whose strength does not depend on the eavesdropper's computing capability, has attracted much attention. We have proposed a chaos modulation method as one PLS method that offers channel coding gain. One alternative is based on polar codes. They are robust error-correcting codes, have a nested structure in the encoder, and the application of this mechanism to PLS encryption (PLS-polar) has been actively studied. However, most conventional studies assume the application of conventional linear modulation such as BPSK, do not use encryption modulation, and the channel coding gain in the modulation is not achieved. In this paper, we propose a PLS-polar method that can realize high-quality transmission and encryption of a modulated signal by applying chaos modulation to a polar-coding system. Numerical results show that the proposed method improves the performance compared to the conventional PLS-polar method by 0.7dB at a block error rate of 10-5. In addition, we show that the proposed method is superior to conventional chaos modulation concatenated with low-density parity-check codes, indicating that the polar code is more suitable for chaos modulation. Finally, it is demonstrated that the proposed method is secure in terms of information theoretical and computational security.

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.

Various types of indices for estimating functional connectivity have been developed over the years that have introduced effective approaches to discovering complex neural networks in the brain. Two significant examples are the phase lag index (PLI) and transfer entropy (TE). Both indices have specific benefits; PLI, defined using instantaneous phase dynamics, achieves high spatiotemporal resolution, whereas transfer entropy (TE), defined using information flow, reveals directed network characteristics. However, the relationship between these indices remains unclear. In this study, we hypothesize that there exists a complementary relationship between PLI and TE to discover new aspects of functional connectivity that cannot be detected using either PLI or TE. To validate this hypothesis, we evaluated the synchronization in a coupled Rössler model using PLI and TE. Consequently, we proved the existence of non-linear relationships between PLI and TE. Both indexes exhibit a specific trend that demonstrates a linear relationship in the region of small TE values. However, above a specific TE value, PLI converges to a constant irrespective of the TE value. In addition to this relational difference in synchronization, there is another characteristic difference between these indices. Moreover, by virtue of its finer temporal resolution, PLI can capture the temporal variability of the degree of synchronization, which is called dynamical functional connectivity. TE lacks this temporal characteristic because it requires a longer evaluation period in this estimation process. Therefore, combining the advantages of both indices might contribute to revealing complex spatiotemporal functional connectivity in brain activity.

In recent years, there has been significant interest in information-theoretic security techniques that encrypt physical layer signals. We have proposed chaos modulation, which has both physical layer security and channel coding gain, as one such technique. In the chaos modulation method, the channel coding gain can be increased using a turbo mechanism that exchanges the log-likelihood ratio (LLR) with an external concatenated code using the max-log approximation. However, chaos modulation, which is a type of Gaussian modulation, does not use fixed mapping, and the distance between signal points is not constant; therefore, the accuracy of the max-log approximated LLR degrades under poor channel conditions. As a result, conventional methods suffer from performance degradation owing to error propagation in turbo decoding. Therefore, in this paper, we propose a new LLR clipping method that can be optimally applied to chaos modulation by limiting the confidence level of LLR and suppressing error propagation. For effective clipping on chaos modulation that does not have fixed mappings, the average confidence value is obtained from the extrinsic LLR calculated from the demodulator and decoder, and clipping is performed based on this value, either in the demodulator or the decoder. Numerical results indicated that the proposed method achieves the same performance as the one using the exact LLR, which requires complicated calculations. Furthermore, the security feature of the proposed system is evaluated, and we observe that sufficient security is provided.

In the fifth-generation mobile communications system (5G), it is critical to ensure wireless security as well as large-capacity and high-speed communication. To achieve this, a chaos modulation method as an encrypted and channel-coded modulation method in the physical layer is proposed. However, in the conventional chaos modulation method, the decoding complexity increases exponentially with respect to the modulation order. To solve this problem, in this study, a hybrid modulation method that applies quadrature amplitude modulation (QAM) and chaos to reduce the amount of decoding complexity, in which some transmission bits are allocated to QAM while maintaining the encryption for all bits is proposed. In the proposed method, a low-complexity decoding method is constructed by ordering chaos and QAM symbols based on the theory of index modulation. Numerical results show that the proposed method maintains good error-rate performance with reduced decoding complexity and ensures wireless security.

This paper studies a novel approach to analysis of switched dynamical systems in perspective of bifurcation and multiobjective optimization. As a first step, we analyze a simple switched dynamical system based on a boost converter with photovoltaic input. First, in a bifurcation phenomenon perspective, we consider period doubling bifurcation sets in the parameter space. Second, in a multiobjective optimization perspective, we consider a trade-off between maximum input power and stability. The trade-off is represented by a Pareto front in the objective space. Performing numerical experiments, relationship between the bifurcation sets and the Pareto front is investigated.

Various types of synchronization phenomena have been reported in coupled chaotic systems. In recent years, the applications of these phenomena have been advancing for utilization in sensor network systems, secure communication systems, and biomedical systems. Specifically, chaos-chaos intermittency (CCI) synchronization is a characterized synchronization phenomenon. Previously, we proposed a new chaos control method, termed as the “reduced region of orbit (RRO) method,” to achieve CCI synchronization using external feedback signals. This method has been gathering research attention because of its ability to induce CCI synchronization; this can be achieved even if internal system parameters cannot be adjusted by external factors. Further, additive stochastic noise is known to have a similar effect. The objective of this study was to compare the performance of the RRO method and the method that applies stochastic noise, both of which are capable of inducing CCI synchronization. The results showed that even though CCI synchronization can be realized using both control methods under the induced attractor merging condition, the RRO method possesses higher adoptability and accomplishes a higher degree of CCI synchronization compared to additive stochastic noise. This advantage might facilitate the application of synchronization in coupled chaotic systems.

The OGY method is one of control methods for a chaotic system. In the method, we have to calculate a target periodic orbit embedded in its chaotic attractor. Thus, we cannot use this method in the case where a precise mathematical model of the chaotic system cannot be identified. In this case, the delayed feedback control proposed by Pyragas is useful. However, even in the delayed feedback control, we need the mathematical model to determine a feedback gain that stabilizes the periodic orbit. Thus, we propose a reinforcement learning algorithm to the design of a controller for the chaotic system. Recently, reinforcement learning algorithms with deep neural networks have been paid much attention to. Those algorithms make it possible to control complex systems. We propose a controller design method consisting of two steps, where we determine a region including a target periodic point first, and make the controller learn an optimal control policy for its stabilization. The controller efficiently explores its control policy only in the region.

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.

It is well-known that chaos synchronization in coupled chaotic systems arises from conditions with specific coupling, such as complete, phase, and generalized synchronization. Recently, several methods for controlling this chaos synchronization using a nonlinear feedback controller have been proposed. In this study, we applied a proposed reducing range of orbit feedback method to coupled cubic maps in order to control synchronization of chaos-chaos intermittency. By evaluating the system's behavior and its dependence on the feedback and coupling strength, we confirmed that synchronization of chaos-chaos intermittency could be induced using this nonlinear feedback controller, despite the fact that the asynchronous state within a unilateral attractor is maintained. In particular, the degree of synchronization is high at the edge between the chaos-chaos intermittency parameter region for feedback strength and the non-chaos-chaos intermittency region. These characteristics are largely maintained on large-scale coupled cubic maps.

Low-density chaotic binary sequences generated by Bernoulli map are discussed in this paper. We theoretically evaluate auto-correlation functions of the low-density chaotic binary sequences based on chaos theory.

A Lévy search strategy based chaotic artificial bee colony algorithm (LABC) is proposed in this paper. The chaotic sequence, global optimal mechanism and Lévy flight mechanism were introduced respectively into the initialization, the employed bee search and the onlooker bee search. The experiments show that the proposed algorithm performed better in convergence speed, global search ability and optimization accuracy than other improved ABC.