Search

The differential chaos shift keying with code index modulation (CIM-DCSK) using Walsh codes can increase the data rate, but error rate performance degrades over practical multipath channel with high delay spread. To tackle this drawback, this paper proposes a parallel CIM-DCSK (PT-CIM-DCSK), where the first time slot is used to transmit the chaotic reference sequence, and the second slot is used to transmit the multiple sequences carrying data bits. In particular, multiple $q$ chaotic sequences are added for data transmission in parallel, and each sequence is modulated by CIM-DCSK with $m_{c}$ bits. By exploiting the quasi-orthogonal characteristics of permuted chaotic signals, the interference between $q$ sequences can be remarkably suppressed. In this way, given the data rate, PT-CIM-DCSK can achieve a larger length of Walsh segment than the CIM-DCSK, since its parallel transmission compensates the rate. In addition, the error performance of the proposed scheme over the multipath Rayleigh fading channel is theoretically analyzed. The theoretical and consistent simulation results demonstrate that the PT-CIM-DCSK can obtain significant performance gains over the conventional CIM-DCSK, and the gain can be up to 5 dB in multipath fading channel with high delay. This is because the larger Walsh segment of PT-CIM-DCSK provides the enhanced robustness against multipath effect. The performance superiority of the proposed scheme is further verified in practical ultra-wideband (UWB) wireless industrial scenarios, which suggests promising for low-cost and low-complexity wireless communication applications. [ABSTRACT FROM AUTHOR]

Consistent distribution of shadows on the surface of the shaded PV array enhances the array’s harvested capacity. Therefore, in this paper, an Image processing inspired Chaos Map reconfiguration is proposed to mitigate the effect of shading. The proposed reconfiguration is aimed at achieving uniform row current when compared with the other conventional configurations with physical relocation of panels without changing the electrical connections. The efficacy of the proposed method is tested on Short Wide, Short Narrow, Long Wide and Long Narrow shading conditions on the basis of both software and hardware results. The proposed method enhanced output metrics under partially shaded conditions and gives most effective dispersion of shading over entire PV array. This proposed method is also compared with other existing static reconfiguration techniques for the above said shading conditions and the results show tremendous increment in output power under both hardware and software platforms. The results replicate that the proposed configuration can be generalized for any size of an SPV Array and output parameters can be enhanced by physical relocation under any sort of shading conditions. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm based on the partial least square (PLS) techniques and the arbitrary polynomial chaos expansion (aPCE) for the probabilistic power flow (PPF) analysis of a power system having many uncertain variables. The proposed method uses the nonlinear PLS to transform a set of random input variables to a smaller number of de-correlated random variables. Then, the aPCE technique is applied to generate the basis polynomial functions and build a surrogate model of the power system response. The algorithm has been implemented and tested with the modified IEEE 118-bus and European 1354-bus systems. The numerical results indicate that, similar to the sparse PCE method and the low-rank approximation technique, the proposed method can be applied to high-dimensional PPF problems. Nonetheless, the proposed approach uses smaller computation time, and estimates statistical characteristics of the response with higher accuracy. [ABSTRACT FROM AUTHOR]

In this paper, an improved Quadrature Multi-carrier Differential Chaos Shift Keying (QMC-DCSK) based on Chaotic Shape-forming Filter (CSF) and Cross Correction (CC) is proposed. The chaotic signal generated by CSF is used as reference spreading sequence in QMC-DCSK. Quadrature multi-carriers are used to carry the reference and multiple information bearing signals simultaneously in order to improve the Bit Transmission Rate (BTR). By this way, the proposed system is able to transmit $2M-1$ bits Traditional Data Stream (TDS) during one traditional DCSK bit duration, where $M$ is the number of carrier frequencies. Meanwhile, the reference signal transmits Additional Data Stream (ADS) encoded by CSF together with $2M-1$ identical or inverse data stream carried by the rest $2M-1$ channels (information bearing signals). By this system configuration, the channel redundance can be used to improved bit error rate (BER) performance of ADS, after decoding TDS. In turn, the TDS reliability can also be improved by checking most ADS polarity of the corresponding carrier. This process is referred to as CC. The contribution of this work lies in the CC operation, by which the reliability of both TDS and ADS is improved significantly. It is the CSF and multi-carrier that make CC possible. The analytical BER is derived for the proposed method. The merits of the proposed system include, first, it improves the BTR as compared to that of QMC-DCSK, because ADS conveys more information bits; second, the ADS reliability is improved dramatically because the $\text{2}\,M$ duplication can be used to improve the signal to noise ratio; third, the TDS reliability is improved as well because the information bits conveyed by each carrier frequency is enhanced and corrected by the $\text{2}\,M$ repetitions. By this way, not only TDS and ADS are transmitted (i.e., the higher BTR is achieved), but also both reliability are improved (i.e. the lower BER is achieved). In order to testify the feasibility and superiority of the proposed method, simulation and wireless open-access research platform (WARP) experiment are conducted. The simulation and experiment results show that the proposed method is superior to other comparison methods. [ABSTRACT FROM AUTHOR]

As a potential technology in weak signal detection (WSD), the chaos theory benefits from its characteristics of the sensitivity to the initial condition and the immunity to the Additive White Gaussian Noise (AWGN). Traditional methods based on chaos theory perform well on single non-variable-frequency signal detection (SNVFSD), which is a common situation in texture flaw detection while it is a rare scenario in the communication field. In this paper, we give a comprehensive analysis of the chaos-based approach for weak signal frequency detection. To better understand the advantages and limitations of the chaos theory, we present the research results for several typical communication scenarios. Specifically, we proposed several chaos-based approaches to get a satisfying performance in the following situations: single variable-frequency signal detection (SVFSD), multiple non-variable-frequency signals detection (MNVFSD), multiple variable-frequency signals detection (MVFSD). To enhance the generalization performance to real application, the critical state's characteristics, Lyapunov Exponents (LE) and Melnikov method are analyzed to employed in these proposed chaos-based approaches. By theoretical analysis and numerical simulations, we study the performance of chaos-based detection systems in terms of SVFSD, MNVFSD, MVFSD. Our results show that these proposed schemes can obtain a satisfying performance in terms of accuracy and robustness, and the extensive simulations demonstrate their effectiveness. [ABSTRACT FROM AUTHOR]

Chaos-based encryption is a promising approach to secure communication due to its complexity and unpredictability. However, various challenges lie in the design and implementation of efficient, low-power, attack-resistant chaos-based encryption schemes with high encryption and decryption rates. In addition, Machine learning (ML) has emerged as a promising tool for enhancing the growing security and efficiency concerns and maximizing the potential of emerging computing platforms across diverse domains. With the rapid advancements in technology and the increasing complexity of computing systems, ML offers a unique approach to addressing security challenges and optimizing performance. This paper presents a comprehensive study on the application of ML techniques to secure chaotic communication for wearable devices, with an emphasis on chaos-based encryption. The theoretical foundations of ML for secure chaotic communication are discussed, including the use of ML algorithms for signal synchronization, noise reduction, and encryption. Various ML algorithms, such as deep neural networks, support vector machines, decision trees, and ensemble learning methods, are explored for designing chaos-based encryption algorithms. This paper places a greater emphasis on methodological aspects, metrics, and performance evaluation of machine learning algorithms. In addition, the paper presents an in-depth investigation into state-of-the-art ML-assisted defense and attacks on chaos-based encryption schemes, covering their theoretical foundations and practical implementations. Furthermore, a review of the potential advantages and limitations associated with the utilization of ML techniques in secure communication systems and encryption is provided. The study extends to exploring the diverse range of applications that can benefit from ML-assisted encryption, such as secure communication in the Internet of Things (IoTs), cloud computing, and wireless networks. Overall, we provide insights into the applications of ML for secure chaotic communication in wearable devices, its challenges, and opportunities, offering a foundation for further research and development and facilitating advancements in the field of secure chaotic communication.

The issue of information security in photonics environment has attracted more and more attention, especially when the secure communication of optical digital images has become a research hotspot. In this paper, we propose a hybrid encryption scheme for color images in the frequency and spatial domains based on double random transform and memristor hyperchaotic system. Firstly, we decompose the color image into RGB channels and then perform fast fourier transform (FFT) to transform the digital image from the spatial domain to the frequency domain. Secondly, two-phase masks are generated using the memristor hyperchaotic system, and the Fresnel diffraction optical transformation method is performed twice for encryption. Thirdly, the transformation from the frequency domain to the spatial domain is completed using inverse fast fourier transform (IFFT). Finally, the image is permuted and diffused using the chaotic sequences to obtain the final cipher image. Double random phase encryption expands the key space, while the combination of spatial and frequency domains improves the resistance to attacks. Based on cryptanalysis theory, we introduce a dynamic key associated with plain image, which can effectively resist plain attack. The experimental results show that the optical digital image encryption scheme has a large key space, excellent comprehensive performance, and can resist common attacks. In addition, we verify the hardware feasibility and ease of implementation of the proposed algorithm in an embedded optical communication network experimental platform. Therefore, our proposed scheme in this paper is a preferred optical digital image secure communication technology scheme with good application prospects.

As chaotic systems are widely used in many fields, the study of them is becoming more and more in- depth. This paper first presents a new single-equilibrium chaotic system which is only three terms, and some fundamental dynamical feature of the new chaotic system are discussed, such as equilibria, dissipativity, Poincaré diagram, bifurcation graph, etc. Secondly, a new finite-time controllers is designed by using Lyapunov stability theory, and it can be used for bound synchronization of the general chaotic systems. In contrast to the current finite time controller of the chaotic system, the designed controller in this paper does not contain exponential term, it can be simple and eliminate the chattering phenomenon during synchronizationis, which may be easier to implement in practical application. In addition, under the finite time controller, the bound of control energy consumption of the chaotic system is estimated. Finally, the finite-time controllers for the new chaotic system are advanced using the design method of finite-time controller of the general chaotic system, and the result of numerical simulation is given to check its validity by the designed method.

This paper describes systematic design process toward third-order autonomous deterministic hyperchaotic oscillators with two coupled generative two-terminal elements. These active devices represent alternative to conventional dissipative accumulation elements such as non-ideal capacitors and inductors. Analyzed network structures contain generalized bipolar transistor as only active element. Three different networks are studied, depending on common-electrode configurations. In each case, transistor is modelled as two-port using admittance parameters with the non-zero linear backward and polynomial forward trans-conductance. As proved in paper, scalar nonlinearity caused by the amplification property of transistor can push circuit into chaotic and, more interestingly, hyperchaotic steady states. Existence of parameter spaces leading to robust chaotic and hyperchaotic solution is documented by using concept of one-dimensional Lyapunov exponents and colored high-resolution surface-contour plots of two largest numbers. Geometrical structural stability of generated strange attractors is proved via construction of the flow-equivalent chaotic oscillator and real measurement. Plane projections of carefully selected strange attractors were captured by oscilloscope and visualized.

In this paper, a novel approach to generating keys for securing color information by combining discrete wavelet transform (DWT) in conjunction with chaotic functions is presented. This procedure is based on chaotic sequences derived using initial conditions and control parameters of the Logistic map function, which are utilized to decompose in different frequency subbands by applying the DWT. These subbands construct the chaotic encoded directional phase masks (CEDPM) keys. To investigate the potential applications of the CEDPM keys, a nonlinear optical cryptosystem for securing color images has been developed. The color image to be encoded in this study is first separated into three color planes such as red (R), green (G), and blue (B) which are transformed into the phase function using a modified phase retrieval algorithm. Subsequently, for R, G, and B color planes in the encoding procedure, the obtained CEDPM keys are employed, correspondingly. This procedure helps to facilitate the creation of a real-value ciphertext for the color channels R, G, and B. These encrypted images, which correspond to the color channels R, G, and B, are positioned at the horizontal, vertical, and diagonal subbands to combine with low-frequency subbands. After that, inverse wavelet operations are carried out to produce a single covered image. This technique strengthens the system’s security by adding an additional layer. The efficacy of the color encryption approaches is confirmed using computer simulations. The results and analysis show that the proposed scheme performs satisfactorily in protecting color image components compared to the other techniques in this area.

This paper is focused on nonlinear behavior associated with fourth-order autonomous lumped circuit known as the Reinartz oscillator. It is shown that this naturally sinusoidal oscillator with three-winding transformer can exhibit robust chaotic behavior. Essential scalar polynomial nonlinearity is not intrinsic to transformer, but to active two-port element described by impedance parameters. The existence of complex solutions is proved on numerical as well as experimental basis. In the first case, conventional routines for qualitative analysis of dynamical flows were applied, based on either prescribed set of differential equations or generated data sequence. In detail, a pair of the largest Lyapunov exponents are visualized with respect to key system parameters, attractor dimensions, recurrence plots and bifurcation diagrams showing interesting routes-to-chaos scenarios are provided to illustrate complexity of observed steady state motion. For the second case, electronic circuits dynamically equivalent to investigated mathematical model will be designed, constructed, and experimentally measured. Chaotic signals captured as oscilloscope screenshots will be compared to theoretical counterparts.

This paper proposes a new chaos-based extremum coding method to realize a true random number generator (RNG). Based on the chain rule, we innovatively introduce two parameters into the dynamics of chaotic systems to modulate the speed and amplitude of state responses. Then, by discretizing the continuous modulated chaotic system, the corresponding discrete chaotic system can be obtained, which allows the use of low-cost micro-controllers for implementation, enhancing system stability, and reducing costs. Also, a novel chaos-based extremum coding approach is proposed for generating a random extremum-coded sequence (RECS). Using this RECS to switch and decide modulation parameters significantly improves the randomness of the sequences generated by the RNGs. To highlight the contribution of this RNG design, the randomness and security of the RNGs are evaluated by statistical tests such as NIST, Diehard, and ENT. Through comparisons with recent published works, the results show that the proposed chaotic extremum-coded RNG can demonstrate superior performance with a higher level of randomness.

In the era of big data, protecting digital images from cyberattacks during network transmission is of utmost importance. While various image encryption algorithms have been developed, some remain vulnerable to specific cyber threats. This paper presents an enhanced version of the image encryption algorithm based on bit-plane extraction (BPCPD) to address its vulnerability to chosen-plaintext attacks. The proposed cryptographic system encompasses three primary phases. The initial phase involves bit-plane extraction from the plaintext image and the generation of random sequences and a random image using multiple chaotic maps, such as the chaotic Arnold map and the chaotic CAT map. The second phase is dedicated to permutation operations, which comprise three sub-phases: multi-layer permutation, multi-round permutation, and recursive permutation. In the third phase, diffusion is introduced to the permuted image through pixel substitution, coupled with XOR operations performed on the respective bit-planes of the random image. To gauge the efficiency of the proposed encryption scheme, a range of experimental analyses are conducted, including histogram analysis, contrast assessment, entropy measurement, correlation analysis, encryption quality assessment, and investigations into noise attacks and occlusion attacks. The results of these experimental analyses, in comparison to an existing encryption scheme, demonstrate that the proposed framework exceeds both BPCPD and other existing encryption schemes in various aspects of performance.

Exploration is an integral part of learning dynamics which allows algorithms to search a space of solutions. When many algorithms simultaneously explore, this can lead to counter-intuitive effects. This paper contributes an analysis of the influence that exploration has on a multi-agent system of $Q$ -learners in a famous congestion dilemma, the Braess paradox. I find ranges of the exploration rate for which $\epsilon $ -greedy $Q$ -learners show chaotic and oscillatory dynamics which do not converge, and yield better than Nash equilibrium results. I decouple the dynamics endogenous to $Q$ -learning from the exogenous exploration rate $\epsilon $ , and find that $Q$ -learners implicitly coordinate with low exploration rates $\epsilon \in (0, 0.1)$ , but are disrupted in their coordination for larger exploration rates $\epsilon > 0.1$ . The best implicit coordination leads to a 20% reduction in average travel times which approaches the social optimum. I discuss how our results may inform multi-agent algorithm design, fit within a cognitive science perspective of cognitive noise during learning, and provide a mechanistic hypothesis for the lack of empirical evidence of the Braess Paradox in traffic systems.

In this paper, a multivariate cooperative internal mode control method based on RBF neural network (RBF-NN) inverse system is proposed to suppress the chaotic behavior in the power system. Firstly, a seven-dimensional model of the controlled power system including energy storage (ES) and static var compensator (SVC) is constructed, and the chaotic dynamics of the system is analyzed by local bifurcation diagram, attractor phase diagram and timing diagram, and the merging crisis and coexistence of chaotic attractors are found in the power system under the action of the low-frequency power disturbance. Secondly, considering the parameter uncertainties of the power system, an RBF-NN inverse system model of the controlled power system is established based on inverse system theory and neural network theory to realize its pseudo-linearization, and a multivariable cooperative internal mode controller is designed to suppress the chaotic behavior in the power system by combining the ES and the SVC. Finally, the effectiveness and robustness of the proposed chaos suppression control strategy are verified by simulation.

Chaotic path planners are a subset of path planning algorithms that use chaotic dynamical systems to generate trajectories throughout an environment. These path planners are imperative in surveillance tasks in the presence of adversarial agents which require the paths to be unpredictable while at the same time guaranteeing complete coverage of the environments. In the online coverage of unknown terrain, the chaotic path planning algorithms can work without the need of the environment map and the designer has additional control over the generated paths relative to other heuristic coverage path planners such as random-walk algorithms. Although chaotic path planners have been studied over the past two decades, there has not been an updated survey on the advances. This paper presents an up-to-date review by providing: an introduction of commonly used chaotic systems and methods for their manipulation; an overview of obstacle avoidance methods used by chaotic path planners; and a discussion on other applications, challenges, and research gaps.

This paper introduces a novel approach to addressing the security challenges of the Internet of Things (IoT) by presenting a secure Chaos-based lightweight cryptosystem. The proposed design incorporates a Pseudo-Chaotic Numbers Generator combined with the Speck64/128 lightweight block cipher, to meet the stringent requirements of security and lightweight characteristics. First, we subject the cryptosystem to a battery of rigorous tests, including various cryptanalytics such as brute-force, differential attacks, and statistical attacks. The results of these tests clearly demonstrate the cryptosystem’s exceptional security resilience and its capacity to effectively withstand these attacks. Then, the novel cryptosystem architecture, specifically designed for resource-limited applications like IoT, was implemented on a Xilinx PYNQ-Z2 XC7Z020 FPGA platform, which aligns perfectly with the constraints of IoT devices. The investigation comprises a thorough analysis and evaluation of the developed cryptosystem according to the algorithm complexity and the achieved precision, hardware area, maximum operational frequency, throughput, efficiency, and power consumption. The findings prove the effectiveness of our approach in terms of computational complexity, memory requirements, and power consumption. Eventually, after reviewing and comparing our results to the existing literature, our cryptosystem’s superiority becomes evident. The simulation results and performance analysis show that the proposed Chaos-Based Lightweight Cryptosystem (SCBLC) can be considered an ideal choice for securing communication in IoT devices with limited resources, making significant strides toward enhancing IoT network security.

Additive cellular automata over a finite abelian group are a wide class of cellular automata (CA) that are able to exhibit most of the complex behaviors of general CA and they are often exploited for designing applications in different practical contexts. We provide an easy to check algebraic characterization of positive expansivity for Additive Cellular Automata over a finite abelian group. We stress that positive expansivity is an important property that defines a condition of strong chaos for CA and, for this reason, an easy to check characterization of positive expansivity turns out to be crucial for designing proper applications based on Additive CA and where a condition of strong chaos is required. First of all, in the paper an easy to check algebraic characterization of positive expansivity is provided for the non trivial subclass of Linear Cellular Automata over the alphabet $(\mathbb {Z}/m \mathbb {Z})^{n}$ . Then, we show how it can be exploited to decide positive expansivity for the whole class of Additive Cellular Automata over a finite abelian group.

To broaden the stability domain of the H-bridge inverter, a control method of the H-bridge inverter combined with PI and improved power reaching law sliding mode control is studied in this paper. To analyze the complex dynamical behavior of this inverter, firstly, the mathematical model of this system is established and numerical simulation of this model is performed. Secondly, the nonlinear dynamical behavior of this inverter is observed by a bifurcation diagram, folding diagram, stroboscopic diagram, time-domain diagram, and spectral diagram. Thirdly, the stability theory of the system is analyzed by applying the fast-varying stability theorem, and the consistency between the theoretical analysis and numerical simulation further proves the mechanism of nonlinear dynamical behavior occurring in this inverter. Finally, the influence of the circuit parameters: input voltage, load inductance, and load resistance on the nonlinear dynamical behavior of the inverter is analyzed. It is shown that this joint control mode can broaden the operating stability domain of the H-bridge inverter, which provides an important theoretical basis for the design and manufacture of the inverter.

Chaotic systems are widely used in various aspects such as information security, signal processing, and synchronous control. The structural complexity and the chaotic behavior of chaotic systems are two significant factors affecting their practical applications. In this paper, we propose a universal two-dimensional (2D) absolute-cosine chaotic model (ACCM). The 2D-ACCM is composed of a nonlinear bounded cosine function and an absolute value function. It can construct new chaotic maps with simple structures and complex chaotic behaviors on the basis of existing chaotic systems. To verify the effectiveness of the proposed system, we first choose two existing one-dimensional (1D) chaotic maps and one existing 2D chaotic map as the seed maps of the 2D-ACCM to generate two new maps, respectively. The results of chaotic behavior analysis show that these two new maps have more complex chaotic behavior and wider chaotic ranges than seed maps and some advanced chaotic maps. Then a hardware experiment platform based on a field-programmable gate array (FPGA) is used for the hardware implementation of the new maps. Finally, a simple chaos-based pseudo-random number generator (PRNG) is introduced to show the practical application. The experimental results show that the new maps can be easily implemented on the FPGA and the chaos-PRNGs can generate pseudo-random numbers with excellent randomness.

In order to improve the security of image transmission, this paper proposes a self-adaptive image encryption scheme based on chaos and gravitation model. The proposed scheme consists of three stages: key generation stage, double scrambling stage, and double diffusion stage. In the key generation stage, the plaintext-associated key generation mechanism (BPPAKG) based on the bit plane is used to obtain the key associated with the plaintext. Since the key ultimately depends on the plaintext image itself, this scheme has self-adaptability. The first stage of scrambling uses mixed chaotic transform and shift row transform to disturb pixel position, then changes the pixel value of the image based on the concept of gravitation to achieve the first stage of diffusion. To enhance the security performance of the scheme, the traditional encryption structure is extended, and the second stage of scrambling and diffusion is quickly realized by using diagonal scanning transform and XOR operation. Simulation and experimental results show that the scheme has good encryption and decryption performance and strong resistance to attack. In addition, compared with some latest proposed algorithms, it has better security.

In this paper, a novel method is proposed to build an improved 1-D discrete chaotic map called flipped product chaotic system (FPCS) by multiplying the output of one map with the output of a vertically flipped second map. Two variants, each with nine combinations, are shown with trade-off between computational cost and performance. The chaotic properties are explored using the bifurcation diagram, Lyapunov exponent, Kolmogorov entropy, and correlation coefficient. The proposed schemes offer a wider chaotic range and improved chaotic performance compared to the constituent maps and several prior works of similar nature. Wide chaotic window and improved chaotic complexity are two desired characteristics for several security applications as these two characteristics ensure enhanced design space with elevated entropic properties. We present a general Field-Programmable Gate Array (FPGA) design framework for the hardware implementation of the proposed flipped-product schemes and the results show good qualitative agreement with the numerical results from MATLAB simulation. Finally, we present a new Pseudo Random Number Generator (PRNG) using the two variants of the proposed chaotic map and validate their excellent randomness property using four standard statistical tests, namely NIST, FIPS, TestU01, and Diehard.

In this paper, we design an optical chaotic secure communication system with multi-dimensional keys and a complex entropy source, which can allow secure communication working in different modes such as unicast, multicast, and broadcast. In the proposed scheme, amplified spontaneous emission (ASE) noise of the erbium-doped fiber amplifier (EDFA) with sufficient randomness is used as an entropy source to improve the security of the system. And by using the electro-optic delay feedback loops, the key spaces are introduced and the phase distortion is generated, then the data are masked in both phase and intensity fields. As a frequency-dependent group delay (FDGD) module, Gires-Tournois interferometer (G-T I) in the feedback loop can effectively hide the time delay signature (TDS) and achieve additional 1036 key spaces. The influence of different key mismatches on decryption function is numerically investigated, and the results indicate that the broadband nature of ASE noise makes the TDS a very sensitive encryption key, which increases the difficulty of illegal third parties stealing information. And with the help of the wavelength converter and wavelength division multiplexer, secure communication in various modes is successfully realized, which greatly improves the communication efficiency and is suitable for various security places.

In this paper, a new two-dimensional sine-cosine coupling chaos map(2D-SCCM) is proposed. The performance of the proposed two-dimensional chaotic system is analysed by using trajectory distribution maps, Lyapunov exponents, sample entropy and sequence sensitivity, etc. The results show that the 2D-SCCM has better randomness and ergodicity, as well as a wider hyperchaotic range than the existing partial two-dimensional chaos maps. To verify its application in practice, a 2D-SCCM-based color image encryption algorithm is proposed. First, the plain image is used to combine with hash function to generate the key. Then, we construct S-Boxes using the random sequence generated by 2D-SCCM combined with Arnold map. Finally, a color image encryption algorithm is proposed by using the constructed S-Boxes and the chaotic map combined with hash function. Experimental simulations and security tests show that the proposed encryption algorithm has high encryption efficiency and strong security, and can effectively protect images from various attacks.

For high-volume manufacturing, yield estimation is an important design step to determine the effects of uncertainties in the fabrication process. The tolerances associated with the fabrication process are applied to the statistically significant system parameters, and a Monte Carlo (MC) simulation is historically done to accurately estimate the yield. This process becomes computationally very expensive when the number of statistically significant system parameters are either too difficult to intuitively determine or are too high. A nonlinear partial-least-squares-based polynomial chaos expansion (NLPLSs-based PCE) is proposed as a solution for complex antenna yield analysis. NLPLS-based PCE effectively reduces the system dimensionality using NLPLS and simultaneously extracts the statistical information on the same sample set, that is, yield, using PCE. It is also possible to perform a global sensitivity analysis using NLPLS-based PCE surrogates, providing an additional advantage. This method is illustrated using an eight-variable single-frequency patch antenna, an eight-variable dual-band patch antenna, and a 37-variable diplexer requiring 30, 10, and 30 analysis points, respectively, to obtain converged yield estimates. [ABSTRACT FROM AUTHOR]

We study the phase synchronization problem with noisy measurements $Y=z^{*}z^{* { \mathrm {\scriptscriptstyle H} }}+\sigma W\in \mathbb {C}^{n\times n}$ , where $z^{*}$ is an $n$ -dimensional complex unit-modulus vector and $W$ is a complex-valued Gaussian random matrix. It is assumed that each entry $Y_{jk}$ is observed with probability $p$. We prove that an SDP relaxation of the MLE achieves the error bound $(1+o(1))\frac {\sigma ^{2}}{2np}$ under a normalized squared $\ell _{2}$ loss. This result matches the minimax lower bound of the problem, and even the leading constant is sharp. The analysis of the SDP is based on an equivalent non-convex programming whose solution can be characterized as a fixed point of the generalized power iteration lifted to a higher dimensional space. This viewpoint unifies the proofs of the statistical optimality of three different methods: MLE, SDP, and generalized power method. The technique is also applied to the analysis of the SDP for $\mathbb {Z}_{2}$ synchronization, and we achieve the minimax optimal error $\exp \left ({-(1-o(1))\frac {np}{2\sigma ^{2}}}\right)$ with a sharp constant in the exponent. [ABSTRACT FROM AUTHOR]

When a peak-current-mode controlled (PCMC) boost converter operates at $D>0.5$ , instabilities such as bifurcations and chaos severely restrict its operation range. This brief proposed a logarithm-type slope compensation (LTSC) to use small amplitude signal to provide enough compensations. Firstly, with the aim of minimizing the error magnification of the input current, the proposed LTSC is deduced. Secondly, the comparisons between the proposed LTSC and other slope compensation (SC) methods are made. Finally, simulations and experiments are carried out to verify the theoretical analysis. The research offered a novel SC to suppress instabilities in PCMC boost converter when $D>0.5$. The proposed LTSC has advantages such as: (1) LTSC uses smaller amplitude to stabilize the converter; (2) LTSC extend the stable region of boost converter; (3) LTSC can be applied in other PCMC dc-dc converters. [ABSTRACT FROM AUTHOR]

Dynamic and nonlinear systems are emerging as potential candidates for random bit generation. In this context, chaotic systems, which are both dynamic and stochastic, are particularly suitable. This article introduces a new continuous chaotic system along with its corresponding implementation, which targets FPGA (fpga). This chaotic system has five dimensions, which exhibit complex chaotic dynamics, thus enabling the utilization of chaotic signals in cryptography. A mathematical analysis is presented to demonstrate the dynamic characteristics of the proposed hyperchaotic system. A novel digital implementation of the proposed system is presented. Moreover, a data scrambling circuit is implemented to eliminate the bias effect and increase the randomness of the bitstream generated from the chaotic signals. We show that the proposed random bit generator has high randomness. The generated bits successfully pass well-known statistical randomness test-suites, i.e., NIST SP800-22, Diehard, and TestU01. The ready-to-use random bit generator is deployed on a Xilinx Zynq-7000 SoC ZC702 Evaluation Kit. Experimental results show that the proposed random bit generator can achieve a maximum throughput of 6.78 Gb/s, which is over 3.6 times greater than state-of-the-art designs, while requiring under 4% of the resources available on the targeted FPGA. [ABSTRACT FROM AUTHOR]

An efficient probabilistic energy flow (PEF) analysis method is proposed for integrated electricity and gas systems (IEGSs) in this letter. A network decoupling based deterministic energy flow (DEF) calculation method is developed. A PEF analysis method is presented based on stochastic response surface method (SRSM). The computational efficiency and convergence performance of DEF and PEF are largely improved. The correctness and effectiveness of the proposed method are verified by using three test systems. [ABSTRACT FROM AUTHOR]

We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications. FGNs interpolate continuously between the popular purely random geometric graphs (a.k.a. the Poisson Boolean network), and random graphs with increasingly fractal behavior. In fact, they form a parametric family of sparse random geometric graphs that are parametrized by a fractality parameter $\nu $ which governs the strength of the fractal structure. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right. We asymptotically characterize the expected number of edges, triangles, cliques and hub-and-spoke motifs in FGNs, unveiling a distinct pattern in their scaling with the size parameter of the network. We then examine the natural question of detecting the presence of fractality and the problem of parameter estimation based on observed network data, in addition to fundamental properties of the FGN as a random graph model. We also explore fractality in community structures by unveiling a natural stochastic block model in the setting of FGNs. Finally, we substantiate our results with phenomenological analysis of the FGN in the context of available scientific literature for fractality in networks, including applications to real-world massive network data. [ABSTRACT FROM AUTHOR]

We study the entanglement dynamics of quantum many-body systems and prove the following: (I) For any geometrically local Hamiltonian on a lattice, starting from a random product state the entanglement entropy is bounded away from the maximum entropy at all times with high probability. (II) In a spin-glass model with random all-to-all interactions, starting from any product state the average entanglement entropy is bounded away from the maximum entropy at all times. We also extend these results to any unitary evolution with charge conservation and to the Sachdev-Ye-Kitaev model. Our results highlight the difference between the entanglement generated by (chaotic) Hamiltonian dynamics and that of random states, for the latter is nearly maximal. [ABSTRACT FROM AUTHOR]

We propose and numerically demonstrate an ultrafast secure key distribution based-on random DNA coding and the chaos synchronization in two identical electro-optic oscillators (EO) with common injection. High-quality synchronization between the responses of EOs with extremely sensitivity to the mismatching of time delay and phase bias is observed. It is noted that the random DNA coding and the delay DNA-XOR in the post-processing can greatly amplify the randomness of the synchronized sequences acquired by symmetrically dual-threshold sampling the correlated physical entropies, and enhance the security of key distribution by providing additional encryption. According to our study, high rate key distribution of over 10 Gb/s can be fulfilled with a good consistency, which can be used for the commercial communication networks. [ABSTRACT FROM AUTHOR]

This brief proposes a method of generating custom-shaped attractors, which depends on a planarly rotating V-shape multi-scroll chaotic system with offset boosting and amplitude control, and its FPGA verification. The proposed planarly rotating, translational (offset boostable), and scalable (amplitude controllable) system exhibits a wide basin of attraction and can cover the whole space. Consequently, non-autonomous parameters enable generating attractors of custom-shapes, e.g., letters of the English alphabet as a demonstrating example. Furthermore, non-autonomous parameters are employed to generate attractors with the shape of complete words and sentences. This takes place by generating letter shapes successively and controlling the position and size of each letter. The chaotic behavior is quantified and indicated using spectral entropy. Experimental verification on FPGA shows good hardware resources utilization and throughput. [ABSTRACT FROM AUTHOR]

Continuous memristor has been widely used in chaotic oscillating circuits and neuromorphic computing systems. However, discrete memristor and its coupling discrete map have not been noticed yet. This article presents a discrete memristor and constructs a general two-dimensional memristive map model by coupling the discrete memristor with an existing discrete map. The pinched hysteresis loops of the discrete memristor are demonstrated. Four examples of memristive discrete maps are provided and their coupling strength-relied and memristor initial-boosted complex dynamics are investigated using numerical measures. The evaluation results manifest that the discrete memristor can enhance the chaos complexity and its coupling maps can generate hyperchaos. Particularly, the hyperchaotic sequences can nondestructively be controlled by memristor initial state and the initial-controlled hyperchaos is robust, which is applicable to many chaos-based applications. Additionally, we develop a hardware platform to implement the memristive maps and acquire the four-channel hyperchaotic sequences. We also apply the memristive maps to the application of secure communication and the experiments show that the memristive maps display better performance than some existing discrete maps. [ABSTRACT FROM AUTHOR]

This article considers the synchronization problem of drive–response Lurie systems with sampled output error transmitted through a limited network channel with a one-step packet dropout. Two kinds of strategies, that is, quantizer-based triggered control (without packet dropout) and active quantizer and packet dropout-based triggered control (with one-step packet dropout), are put forward. By thoroughly exploring quantizer, sampling interval, and one-step packet dropout information and merging them together, the quantizer and packet dropout related triggering method is proposed to actively deal with the negative effects caused by packet dropout and sampling sensor. With the proposed method, it is demonstrated that synchronization can be ensured and the output error will always be bounded by the quantizer range. In addition, the relationship between the sensor sampling interval and the triggering parameter is provided to match up with our proposed methods. Lower transmission bit rate is also obtained to save more channel resources. Synchronization of two Chua’s circuits is given as an example to demonstrate the validity of our presented results. [ABSTRACT FROM AUTHOR]