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In recent years, many chaotic image encryption algorithms have been cracked by chosen plaintext attack. Therefore, the method of associating the key with the plaintext to resist the cryptanalysis has received extensive attention from designers. This paper proposes a new method of cryptanalysis for image encryption algorithms with a key associated with plaintext. We broke an image encryption scheme using chaos and DNA encoding. Through our comprehensive security analysis, we found a security vulnerability in the mechanism of the association between the key and plaintext and proposed a breaking scheme. The experimental results show that the chosen plaintext attack can recover the cipher image to the plain image. The cryptanalysis scheme proposed in this paper can provide new ideas for subsequent cryptanalysis work and also provide some meaningful references for designers to improve the security of encryption algorithms when designing them. In addition, we also propose an improved logistic chaotic map with random bit-position scrambling. The improved chaotic map has a wider parameter range and a larger Lyapunov exponent. In the end, some suggestions are given to improve the original algorithm to resist such attacks. [ABSTRACT FROM AUTHOR]

Francis turbines, essential for stability in diverse operating conditions and variable-speed scenarios, encounter efficiency-compromising vortex rope formations in the draft tube, leading to substantial pressure fluctuations. This research delves into the analysis of energy loss and pressure fluctuations associated with these vortex ropes. Employing the local entropy generation rate (LEGR) method and chaos theory, we scrutinize the behaviour of vortex ropes and their resultant pressure fluctuations. Notably, vortex ropes exhibit maximum LEGR near the runner cone, with secondary vortices escalating instability downstream. In the elbow section, the collision of vortex ropes with the outer elbow amplifies LEGR, primarily driven by fluctuating velocities (approximately 90%). Leveraging the GWO-VMD algorithm, non-stationary signals are decomposed, unveiling a significant 1.6 Hz vortex rope frequency under partial load (PL) conditions and isolating external noise frequencies, such as the prominent 300 Hz. Following decomposition, chaos theory tools, including phase space reconstruction and phase trajectory graphs, unveil the chaotic nature of PL conditions attributed to spiral vortex ropes, resulting in profound pressure fluctuations. This study enhances our understanding of such systems and provides methodologies for improved noise reduction and optimization of turbine performance. [ABSTRACT FROM AUTHOR]

This paper presents a hardware-based audio encryption system using a 2D chaotic map and dynamic S-box design implemented on an Artix-7 FPGA platform. Three distinct chaotic maps—logistic–fraction (2D-LF), logistic–sine (2D-LS), and fraction–sine (2D-FS)—were investigated and implemented on an FPGA. The 2D-LF map was employed in the encryption system for its throughput and power efficiency performance. The proposed encryption system benefits from the randomness of chaotic sequences for block permutation and S-box substitution to enhance the diffusion and confusion properties of the encrypted speech signal. The system's encryption strength is validated through performance evaluations, using the mean squared error (MSE), signal-to-noise ratio (SNR), correlation coefficients, and NIST randomness tests, which confirm the unpredictability of the encrypted speech signal. The hardware implementation results show a throughput of 2880 Mbps and power consumption of 0.13 W. [ABSTRACT FROM AUTHOR]

The elementary cellular automata (ECAs) under the chaotic rule possess long periodicity and are widely used in pseudo-random number generators. However, their period is limited, related to the rule and the number of cells. Meanwhile, the Boolean functions of some ECAs are linear and vulnerable to linear analysis. Thus, the ECA cannot be directly implemented in the stream cipher. In this paper, a hybrid ECA (HECA) with dynamic mask (HECA-M) is designed. The HECA-M consists of two parts: the driving and mask parts. The driving part based on a HECA is used in generating the keystream, and the mask part based on a chaotic ECA is utilized to determine the iterative rule of the driving part. Subsequently, a stream cipher based on the HECA-M and SHA-512 is proposed. The statistic and secure analyses indicate that the proposed stream cipher possesses good randomness and can resist stream cipher analyses, such as exhaustive search, Berlekamp–Massey synthesis, guess and determine attack, time–memory–data tradeoff attack, etc. Hence, the proposed scheme can meet security requirements. Moreover, the time and space consumption of the proposed stream cipher is qualified. [ABSTRACT FROM AUTHOR]

The increasingly complex electromagnetic environment of modern warfare and the proliferation of intelligent jamming threaten to reduce the survival rate of radio fuzes on the battlefield. Radio frequency (RF) stealth technology can fundamentally improve the anti-interception and reconnaissance capabilities of radio fuzes, thereby lessening the probability of them being intercepted, recognized, and jammed by the enemy. In this paper, an RF stealth waveform based on chaotic pulse-position modulation is proposed for ultra-wideband (UWB) radio fuzes. Adding a perturbation signal based on the Tent map ensures that the chaotic sequences have sufficiently long periods despite hardware byte limitations. Measuring the approximate entropy and sequence period shows that the Tent map with the addition of perturbation signals can maintain good randomness under byte constraints, closely approximating the Tent map with ideal precision. Simulations verify that the proposed chaotic mapping used to modulate the pulse position of an ultra-wideband radio fuze signal results in superior detection, anti-interception, and anti-jamming performance. [ABSTRACT FROM AUTHOR]

Based on the chaotic polarization system of optically injected cascaded vertical-cavity surface-emitting lasers (VCSELs), we propose a novel implementation scheme for high-speed optical chaotic data selection logic operations. Under the condition where the slave VCSEL (S-VCSEL) outputs a chaotic laser signal, we calculate the range of the applied electric field and the optical injection amplitude. We also investigate the evolution of the correlation characteristics between the polarized light output from the periodic poled LiNbO3 (PPLN) and the S-VCSEL as a function of the optical injection amplitude under different applied electric fields. Furthermore, we analyze the polarization bistability of the polarized light from the PPLN and S-VCSEL. Based on these results, we modulate the optical injection amplitude as the logic input and the applied electric field as the control logic signal. Using a mean comparison mechanism, we demodulate the polarized light from the PPLN and S-VCSEL to obtain two identical logic outputs, achieving optical chaotic data selection logic operations with an operation speed of approximately 114 Gb/s. Finally, we investigate the influence of noise on the logic outputs and find that both logic outputs do not show any error symbols under the noise strength as high as 180 dBw. The anti-noise performance of logic output O1 is superior to that of optical chaotic logic output O2. For noise strengths up to 185 dBw, error symbols in O2 can be detected and corrected by comparison with O1. [ABSTRACT FROM AUTHOR]

Data encryption is an important part of the communication system. The Chaos essential properties, make it a crucial candidate for encryption applications. There is a compromise between complexity and security in previous studies. In this study, high security was achieved with low complexity. This paper proposed a 3D chaotic map and S-Box has been cascaded to get a high efficiency as complex algorithms or multi-iteration schemes. The first stage is ciphering using 3D cat-map, the second stage is S-box based on 3D henon map, while the third stage is another ciphering stage using 3D henon map. In this study, various encryption techniques, including cipher algorithms and substitution box, are combined with the OFDM system to establish a secure image transmission over a Rayleigh fading channel. QPSK modulation is used to ensure the simplicity of the proposed system. Six gray images are used, Lena, the cameraman, Barbara, Baboon, pepper and Elaine for testing and comparing with previous works. Security analysis is performed to evaluate the quality and security of the encryption process, the entropy value reach 7.99, correlation coefficient is around zero and the histogram is uniform. In addition, the key size is 2630. For image transmission evaluation, the PSNR and BER are utilized and it reached 10-5 for BER. According to the statistical results, the proposed image encryption scheme is secure and efficient.

Let G be an abelian semigroup of matrices on K n ( K = C or R ). We show that if G is hypercyclic, then it has no non-zero finite orbit. This result fails if we drop the assumption that G is abelian. As a consequence, if G is abelian, it is not chaotic. On the other hand, we show that G is not minimal for n ≥ 3 , but it can be minimal for n = 1 ; for K = R , the critical number is n = 2 . [ABSTRACT FROM AUTHOR]

The study of extreme events (EEs) in photonics has expanded significantly due to straightforward implementation conditions. EEs have not been discussed systematically, to the best of our knowledge, in the chaotic dynamics of a Fabry–Perot laser with optical feedback, so we address this in the current contribution. Herein, we not only find EEs in all modes but also divide the EEs in total output into two categories for further discussion. The two types of EEs have similar statistical features to conventional rogue waves. The occurrence probability of EEs undergoes a saturation effect as the feedback strength increases. Additionally, we analyze the influence of feedback strength, feedback delay, and pump current on the probability of EEs defined by two criteria of EEs and find similar trends. We hope that this work contributes to a deep understanding and serves as inspiration for further research into various multimode semiconductor laser systems. [ABSTRACT FROM AUTHOR]

It has been reported by World Health Organization (WHO) that the Covid-19 epidemic due to the Sar Cov-2 virus, which started in China and affected the whole world, caused the death of approximately six million people over three years. Global disasters such as pandemics not only cause deaths but also bring other global catastrophic problems. Therefore, governments need to perform very serious strategic operations to prevent both infection and death. It is accepted that even if there are vaccines developed against the virus, it will never be possible to predict very complex spread dynamics and reach a spread pattern due to new variants and other parameters. In the present study, four countries: Türkiye, Germany, Italy, and the United Kingdom have been selected since they exhibit similar characteristics in terms of the pandemic’s onset date, wave patterns, measures taken against the outbreak, and the vaccines used. Additionally, they are all located on the same continent. For these reasons, the three-year Covid-19 data of these countries were analyzed. Detailed chaotic attractors analyses were performed for each country and Lyapunov exponents were obtained. We showed that the three-year times series is chaotic for the chosen countries. In this sense, our results are compatible with the results of the Covid-19 analysis results in the literature. However, unlike previous Covid-19 studies, we also found out that there are chaotic, periodic, or quasi-periodic sub-series within these chaotic time series. The obtained results are of great importance in terms of revealing the details of the dynamics of the pandemic.

Data security is vital if transferred over a wireless network or stored on a personal computer. The essential properties of chaos, such as initial state sensitivity and unpredictability, make it a crucial candidate for encryption applications. This paper proposes a 3D chaotic map and a cascaded S-Box that can be combined to get a high-efficiency and complex cryptographic algorithm. The first stage is ciphering using a 3D cat map, the second stage is an S-box based on a 3D Henon map, and the third stage is another ciphering stage using a 3D Henon map. This study combines various encryption techniques, including cipher algorithms and substitution boxes, with the OFDM system to establish a secure image transmission over a Rayleigh fading channel. BPSK modulation is used to ensure the simplicity of the proposed system. Three grey images are used, Lena, the camera-man, and Pepper, for testing and comparing with previous works. Security analysis is performed to evaluate the quality and security of the encryption process. For image transmission evaluation, the PSNR and BER are utilized. According to the statistical results, the proposed image encryption scheme is secure and efficient. The comparison with the previous studies shows that this system is competitive with previous works.

The elementary cellular automata (ECAs) under the chaotic rule possess long periodicity and are widely used in pseudo-random number generators. However, their period is limited, related to the rule and the number of cells. Meanwhile, the Boolean functions of some ECAs are linear and vulnerable to linear analysis. Thus, the ECA cannot be directly implemented in the stream cipher. In this paper, a hybrid ECA (HECA) with dynamic mask (HECA-M) is designed. The HECA-M consists of two parts: the driving and mask parts. The driving part based on a HECA is used in generating the keystream, and the mask part based on a chaotic ECA is utilized to determine the iterative rule of the driving part. Subsequently, a stream cipher based on the HECA-M and SHA-512 is proposed. The statistic and secure analyses indicate that the proposed stream cipher possesses good randomness and can resist stream cipher analyses, such as exhaustive search, Berlekamp–Massey synthesis, guess and determine attack, time–memory–data tradeoff attack, etc. Hence, the proposed scheme can meet security requirements. Moreover, the time and space consumption of the proposed stream cipher is qualified.

It has been reported by World Health Organization (WHO) that the Covid-19 epidemic due to the Sar-Cov-2 virus, which started in China and affected the whole world, caused the death of approximately six million people over three years. Global disasters such as pandemics not only cause deaths but also bring other global catastrophic problems. Therefore, governments need to perform very serious strategic operations to prevent both infection and death. It is accepted that even if there are vaccines developed against the virus, it will never be possible to predict very complex spread dynamics and reach a spread pattern due to new variants and other parameters. In the present study, four countries: Türkiye, Germany, Italy, and the United Kingdom have been selected since they exhibit similar characteristics in terms of the pandemic's onset date, wave patterns, measures taken against the outbreak, and the vaccines used. Additionally, they are all located on the same continent. For these reasons, the three-year Covid-19 data of these countries were analyzed. Detailed chaotic attractors analyses were performed for each country and Lyapunov exponents were obtained. We showed that the three-year times series is chaotic for the chosen countries. In this sense, our results are compatible with the results of the Covid-19 analysis results in the literature. However, unlike previous Covid-19 studies, we also found out that there are chaotic, periodic, or quasi-periodic sub-series within these chaotic time series. The obtained results are of great importance in terms of revealing the details of the dynamics of the pandemic. [ABSTRACT FROM AUTHOR]

Transformerless grid-connected inverters for photovoltaic (PV) applications provide several advantages such as reduced cost and volume as well as an increased efficiency. However, the removal of the transformer gives rise to several problems related to leakage currents and electromagnetic interferences (EMI). This paper presents different chaotic unipolar sine-pulse width modulation (C-USPWM) techniques for a transformerless grid-connected PV inverter based on parameter selection. The main objective behind this proposed chaotic modulation technique is to reduce the conducted EMI without worsening the power quality and the common-mode voltage (CMV). The method is validated through numerical simulations and experimental tests carried out on laboratory prototype of an optimized H5 inverter (oH5). The obtained results showed its superiority to the conventional unipolar sine-pulse width modulation (USPWM). We showed also that the appropriate parameter selection of the C-UPSWM could advantageously combine an improved EMI performance and an efficient control, making it possible to deliver a significant reduction of the peaks' amplitudes in the frequency spectrum of the common-mode (CM) voltage. [ABSTRACT FROM AUTHOR]

Abstract Recently, medical technologies have developed, and the diagnosis of diseases through medical images has become very important. Medical images often pass through the branches of the network from one end to the other. Hence, high‐level security is required. Problems arise due to unauthorized use of data in the image. One of the methods used to secure data in the image is encryption, which is one of the most effective techniques in this field. Confusion and diffusion are the two main steps addressed here. The contribution here is the adaptation of the deep neural network by the weight that has the highest impact on the output, whether it is an intermediate output or a semi‐final output in additional to a chaotic system that is not detectable using deep neural network algorithm. The colour and grayscale images were used in the proposed method by dividing the images according to the Region of Interest by the deep neural network algorithm. The algorithm was then used to generate random numbers to randomly create a chaotic system based on the replacement of columns and rows, and randomly distribute the pixels on the designated area. The proposed algorithm evaluated in several ways, and compared with the existing methods to prove the worth of the proposed method.

Abstract Background Information security is very important in today’s digital world, especially cybersecurity. The most common requirement in securing data in all services: confidentiality, digital signature, authentication, and data integrity is generating random keys. These random keys should be tested for randomness. Hardware security is more recommended than software. Hardware security has more speed and less exposure to many attacks than software security. Software security is vulnerable to attacks like buffer overflow attacks, side-channel attacks, and Meltdown–Spectre attacks. Results In this paper, we propose an FPGA Implementation for the adaptive digital chaotic generator. This algorithm is proposed and tested before. We introduce its implementation as hardware. This algorithm needs a random number seed as input. We propose two designs. The first one has an input random number. The second one has PRNG inside. The target FPGA is Xilinx Spartan 6 xc6slx9-2-cpg196. We used MATLAB HDL Coder for the design. We propose a configurable Key block’s length. For 32 bit the maximum frequency is 15.711 MHz versus 11.635 MHz for the first and second designs respectively. The area utilization of the Number of Slice Registers is 1% versus 2%. The number of Slice Look Up Tables is 40% versus 59%. number of bonded input output blocks is 64% versus 66%. otherwise are the same for the two designs. Conclusions In this paper, we propose an efficient and configurable FPGA Design for adaptive digital chaotic key generator. Our design has another advantage of storing the output keys internally and reading them later.

Intradural spinal lipoma (ISL) prevalent in children and young adults usually presents with spastic progressive quadriparesis, sensory disturbances, and gait abnormalities. Chaotic lipomas named due to their haphazard distribution are an extremely rare variant of ISL present at the dorsal root entry zone. We describe a case of chaotic spinal lipoma and elucidate the challenges faced in the management of this entity.

Fruit Fly Optimization Algorithm (FOA) is a metaheuristic algorithm inspired by fruit fly foraging behaviours. A large numbers of variants of FOA have been proposed by many researchers. These have been applied to solve various engineering optimization problems. The existing variants and improvements can be categorized as discrete, chaotic, hybrid, improved or modified, and multi-objective. In this paper, a systematic review of FOA has been presented. The review investigates into FOA variants and their pros and cons, as well as FOA applications in various engineering fields. The study is carried out using the PRISMA methodology. The manuscripts have been identified and included in the review using this methodology. In general, researchers around the world confront difficulties in identifying appropriate algorithms to handle real-world optimization problems. This study can be used by researchers to address real-world problems in various domains using FOA, and it can also be used to design variants of FOA and other metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

In this work, we construct a model of an asymmetrically coupled network of semiconductor chaotic lasers in order to recognize noisy digital images of digits 0–9, derived from different samples in the digital image sets 0–9 found within the MNIST dataset. Here, the lasers network consists of eight asymmetrically coupled semiconductor lasers. The chaotic lasers network is driven by the external inputs, which encode one noise digital image to be recognized. The outputs of the chaotic lasers network driven by a total of 40 samples from the digital image sets 0–9 are utilized as ten sets of reference signals. The output of the chaotic lasers network induced by one noisy digital image is used as a test signal. By judging the maximum of the correlations of the test signal with the ten sets of reference signals, all noisy digital images 0–9 can be recognized well under different noises. Moreover, we further explore the recognition rate for each noisy digital image under different noises and a fixed injection strength. It is found that all noisy digital images can be recognized well under a certain low injection strength. The recognition-rates of all noisy digital images can further decrease to a certain extent under higher noise and a fixed the injection strength. The injection strength has little influence on the recognition rate of one noise digital image target with lower noise. The recognition rate under higher noise maintains a higher value (more than 0.9) when the injection strength is smaller than a certain value, but for the larger injection strength, the recognition rate exhibits further decrease. The modeled chaotic lasers network can play the role of photonic accelerators for the recognition of the noisy digital images. [ABSTRACT FROM AUTHOR]

In recent years, there has been an increasing interest in employing chaotic-based random number generators for cryptographic purposes. However, many of these generators produce sequences that lack the necessary strength for cryptographic systems, such as Tent-Map. However, these generators still suffer from common issues when generating random numbers, including issues related to speed, randomness, lack of statistical properties, and lack of uniformity. Therefore, this paper introduces an efficient pseudo-random number generator, called State-Based Tent-Map (SBTM), based on a modified Tent-Map, which addresses this and other limitations by providing highly robust sequences suitable for cryptographic applications. The proposed generator is specifically designed to generate sequences with exceptional statistical properties and a high degree of security. It utilizes a modified 1D chaotic Tent-Map with enhanced attributes to produce the chaotic sequences. Rigorous randomness testing using the Dieharder test suite confirmed the promising results of the generated keystream bits. The comprehensive evaluation demonstrated that approximately 97.4% of the tests passed successfully, providing further evidence of the SBTM's capability to produce sequences with sufficient randomness and statistical properties. [ABSTRACT FROM AUTHOR]

In this paper, modelling of a three-level chaotic supply chain network. This model has the uncertainty of the retailer in the manufacturer. An adaptive neural fuzzy method has been proposed to synchronize the two chaotic supply chain networks. To train adaptive neural fuzzy controller, first, a nonlinear feedback control method is designed. Then, using Lyapanov theory, it is proved that the nonlinear feedback controller can reduce the synchronization error to zero in a finite time. The simulation results show that the proposed neural fuzzy controller architecture well controls the synchronization of the two chaotic supply chain networks. In the other part of the simulation, a comparison is made between the performance of the nonlinear controller and the adaptive neural fuzzy. Also, in the simulation results, the controller signal is depicted. This signal indicates that the cost of implementation in the real world is not high and is easily implemented.

Titanium alloys has significance in engineering applications owing to their enhanced properties and its ability to retain the shape at elevated temperatures. A new Teaching Learning Based Optimization (TLBO) variant was developed with multiple search features to mitigate cutting force and surface irregularities in Titanium samples. This assists to achieve the best quality of the product at minimal cutting energy. Experiments were conducted and the significance of machining parameters on cutting force and surface finish were analyzed. It is ascertained that the best surface is attained at a lower tool feed rate with higher cutting speed. The increase of nose radius has more influence on the surface quality. Chaotic multiobjective TLBO with multiple effective guidance was applied in both single objective and multiobjective optimization, where useful information of other non-fittest learners is leveraged for effective more population search. The performance of the new algorithm was evaluated and comprehensively discussed. The minimum cutting force Fz=65.06N and Ra=1.41μm can be achieved with v =130m/min, f=0.051mm/rev, nr=0.4mm and ap=0.5mm. The predicted results were validated experimentally and verified with other existing optimizers. It is concluded that this new algorithm can be applied in machining and production wastage can be greatly minimized.

Information can be shared across the Internet using cloud computing, a powerful paradigm for meeting the needs of individuals and organizations. To minimize access time and maximize load balancing for data nodes (DNs), a dynamic data replication algorithm is necessary. Even so, few of the existing algorithms consider each objective holistically during replication. An improved ant lion optimizer (ALO) algorithm and a fuzzy system are used in this paper to determine dynamically the number of replicas and the DNs for replication. Further, it balances the trade-offs among different objectives (e.g., service time, system availability, load, and monetary cost). The ALO algorithm has been widely applied to solve complex optimization problems due to its simplicity in implementation. However, ALO has premature convergence and can thus easily get trapped into the local optimum solution. In this paper, to overcome the shortcomings of ALO by balancing exploration and exploitation, a hybrid ant lion optimizer with Tabu search algorithm (ALO-Tabu) is proposed. There are several improvements of the ALO, in which the appropriate solutions are selected for the initial population based on chaotic maps (CMs) and opposition-based learning (OBL) strategies. On the other hand, there are many CMs, OBLs, and random walk strategies that make it difficult to select the best one for optimization. Generally, they are selected manually, which is time-consuming. As a result, this paper presents a hyper-heuristic ALO (HH-ALO-Tabu) that automatically chooses CMs, OBLs, and random walk strategies depending on the differential evolution (DE) algorithm. Based on 20 well-known test functions, the experiment results and statistical tests show that HH-ALO-Tabu can solve optimization problems effectively. [ABSTRACT FROM AUTHOR]

Background: Information security is very important in today's digital world, especially cybersecurity. The most common requirement in securing data in all services: confidentiality, digital signature, authentication, and data integrity is generating random keys. These random keys should be tested for randomness. Hardware security is more recommended than software. Hardware security has more speed and less exposure to many attacks than software security. Software security is vulnerable to attacks like buffer overflow attacks, side-channel attacks, and Meltdown–Spectre attacks. Results: In this paper, we propose an FPGA Implementation for the adaptive digital chaotic generator. This algorithm is proposed and tested before. We introduce its implementation as hardware. This algorithm needs a random number seed as input. We propose two designs. The first one has an input random number. The second one has PRNG inside. The target FPGA is Xilinx Spartan 6 xc6slx9-2-cpg196. We used MATLAB HDL Coder for the design. We propose a configurable Key block's length. For 32 bit the maximum frequency is 15.711 MHz versus 11.635 MHz for the first and second designs respectively. The area utilization of the Number of Slice Registers is 1% versus 2%. The number of Slice Look Up Tables is 40% versus 59%. number of bonded input output blocks is 64% versus 66%. otherwise are the same for the two designs. Conclusions: In this paper, we propose an efficient and configurable FPGA Design for adaptive digital chaotic key generator. Our design has another advantage of storing the output keys internally and reading them later. [ABSTRACT FROM AUTHOR]

Feature selection is a crucial process in machine learning and data mining that identifies the most pertinent and valuable features in a dataset. It enhances the efficacy and precision of predictive models by efficiently reducing the number of features. This reduction improves classification accuracy, lessens the computational burden, and enhances overall performance. This study proposes the improved binary golden jackal optimization (IBGJO) algorithm, an extension of the conventional golden jackal optimization (GJO) algorithm. IBGJO serves as a search strategy for wrapper-based feature selection. It comprises three key factors: a population initialization process with a chaotic tent map (CTM) mechanism that enhances exploitation abilities and guarantees population diversity, an adaptive position update mechanism using cosine similarity to prevent premature convergence, and a binary mechanism well-suited for binary feature selection problems. We evaluated IBGJO on 28 classical datasets from the UC Irvine Machine Learning Repository. The results show that the CTM mechanism and the position update strategy based on cosine similarity proposed in IBGJO can significantly improve the Rate of convergence of the conventional GJO algorithm, and the accuracy is also significantly better than other algorithms. Additionally, we evaluate the effectiveness and performance of the enhanced factors. Our empirical results show that the proposed CTM mechanism and the position update strategy based on cosine similarity can help the conventional GJO algorithm converge faster. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study the soliton solutions and dynamics analysis of the fractional Radhakrishnan–Kundu–Lakshmanan equation with multiplicative noise in the Stratonovich sense. Firstly, the wave transformation is used to obtain the nonlinear ordinary differential equation, and then the nonlinear ordinary differential equation is transformed into a two-dimensional plane dynamic system with a Hamiltonian system. Secondly, the phase portrait and sensitivity of the plane dynamic system and its perturbed system are studied using Maple software. Thirdly, the soliton solutions of the stochastic fractional Radhakrishnan–Kundu–Lakshmanan equation can be constructed, and the Jacobian function solutions and hyperbolic function solutions are obtained. Finally, some three-dimensional and two-dimensional diagrams of the obtained solutions are also drawn. Moreover, the modulation stability of the equation under consideration is also given.

The main purpose of this paper is to study the dynamics and embedded solitons of stochastic quadratic and cubic nonlinear susceptibilities in the Itô sense, which can further help researchers understand the propagation of soliton nonlinear systems. Firstly, a two-dimensional dynamics system and its perturbation system are obtained by using a traveling wave transformation. Secondly, the phase portraits of the two-dimensional dynamics system are plotted. Furthermore, the chaotic behavior, two-dimensional phase portraits, three-dimensional phase portraits and sensitivity of the perturbation system are analyzed via Maple software. Finally, the embedded solitons of stochastic quadratic and cubic nonlinear susceptibilities are obtained. Moreover, three-dimensional and two-dimensional solitons of stochastic quadratic and cubic nonlinear susceptibilities are plotted. [ABSTRACT FROM AUTHOR]

In this paper, modeling of a three-level chaotic supply chain network. This model has the uncertainty of the retailer in the manufacturer. An adaptive neural fuzzy method has been proposed to synchronize the two chaotic supply chain networks. First, a nonlinear feedback control method is designed to train an adaptive neural fuzzy controller. Then, using Lyapunov theory, it is proved that the nonlinear feedback controller can reduce the synchronization error to zero in a finite time. The simulation results show that the proposed neural fuzzy controller architecture well controls the synchronization of the two chaotic supply chain networks. In the other part of the simulation, a comparison is made between the performance of the nonlinear controller and the adaptive neural fuzzy. Also, in the simulation results, the controller signal is depicted. This signal indicates that the cost of implementation in the real world is not high and is easily implemented. [ABSTRACT FROM AUTHOR]

Based on the chaotic polarization system of optically injected cascaded vertical-cavity surface-emitting lasers (VCSELs), we propose a novel implementation scheme for high-speed optical chaotic data selection logic operations. Under the condition where the slave VCSEL (S-VCSEL) outputs a chaotic laser signal, we calculate the range of the applied electric field and the optical injection amplitude. We also investigate the evolution of the correlation characteristics between the polarized light output from the periodic poled LiNbO3 (PPLN) and the S-VCSEL as a function of the optical injection amplitude under different applied electric fields. Furthermore, we analyze the polarization bistability of the polarized light from the PPLN and S-VCSEL. Based on these results, we modulate the optical injection amplitude as the logic input and the applied electric field as the control logic signal. Using a mean comparison mechanism, we demodulate the polarized light from the PPLN and S-VCSEL to obtain two identical logic outputs, achieving optical chaotic data selection logic operations with an operation speed of approximately 114 Gb/s. Finally, we investigate the influence of noise on the logic outputs and find that both logic outputs do not show any error symbols under the noise strength as high as 180 dBw. The anti-noise performance of logic output O1 is superior to that of optical chaotic logic output O2. For noise strengths up to 185 dBw, error symbols in O2 can be detected and corrected by comparison with O1.

The study of extreme events (EEs) in photonics has expanded significantly due to straightforward implementation conditions. EEs have not been discussed systematically, to the best of our knowledge, in the chaotic dynamics of a Fabry–Perot laser with optical feedback, so we address this in the current contribution. Herein, we not only find EEs in all modes but also divide the EEs in total output into two categories for further discussion. The two types of EEs have similar statistical features to conventional rogue waves. The occurrence probability of EEs undergoes a saturation effect as the feedback strength increases. Additionally, we analyze the influence of feedback strength, feedback delay, and pump current on the probability of EEs defined by two criteria of EEs and find similar trends. We hope that this work contributes to a deep understanding and serves as inspiration for further research into various multimode semiconductor laser systems.

The main objective of this paper is to study the chaotic behavior and embedded soliton of cubic-quartic χ(2) and χ(3) nonlinear susceptibilities with multiplicative white noise. Firstly, traveling wave transformation and the trial equation method are used to obtain the nonlinear ordinary differential equations. Secondly, chaotic behavior, bifurcation and sensitivity of the perturbed perturbation system are studied. Thirdly, the embedded soliton solutions of cubic-quartic χ(2) and cubic χ(3) nonlinear model can be obtained.

Biological systems, composed of various interrelated components, are nonlinear systems. Improved disease diagnosis and the application of efficient treatment and therapeutic aids are the direct outcomes of possessing a deep understanding of such systems. Therefore, by employing diverse biological system simulations and subsequently analyzing their responses and characteristics, we can diagnose diseases. In this particular study, a novel stimulation method was utilized for the first time, employing the Rossler equation, to record the electromyogram (EMG) signals of the biceps muscle in ten participants. The presented dataset enables the extraction of biological, computational, and chaotic features, which can be utilized for disease classification and diagnosis. Furthermore, this dataset can be employed for the training, validation, and testing of neural networks.

This paper introduces the generalized fractional differential quadrature method, which is based on the generalized Caputo type and is used for the first time to solve nonlinear fractional differential equations. One of the effective shape functions of this method is the Cardinal Sine shape function, which is used in combination with the fractional operator of the generalized Caputo kind to convert nonlinear fractional differential equations into a nonlinear algebraic system. The nonlinearity problem is then solved using an iterative approach. Numerical results for a variety of chaotic systems are introduced using the MATLAB program and compared with previous theoretical and numerical results to ensure their reliability, convergence, accuracy, and efficiency. The fractional parameters play an effective role in studying the proposed problems. The achieved solutions prove the viability of the presented method and demonstrate that this method is easy to implement, effective, highly accurate, and appropriate for studying fractional differential equations emerging in fields related to chaotic systems and generalized Caputo-type fractional problems in the future. [ABSTRACT FROM AUTHOR]

In this paper, the coupled Kundu–Mukherjee–Naskar equation is considered, which is usually used to describe the oceanic rogue waves, hole waves and Bragg grating fibers. Firstly, the traveling wave transformation is applied to convert the coupled Kundu–Mukherjee–Naskar equation into two-dimensional planar dynamic system. Secondly, bifurcation and two-dimensional phase portrait of the coupled Kundu–Mukherjee–Naskar equation are discussed by using the plane dynamics system. What is more, after adding periodic perturbation term, two-dimensional phase portrait, three-dimensional phase portrait, Poincaré section and sensitivity of its perturbed system are plotted by the Maple software. Finally, the optical soliton solutions of the coupled Kundu–Mukherjee–Naskar equation are obtained by using planar dynamical system method.

In this paper, coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion is introduced, which is usually used to simulate the propagation model of pulses’ temporal evolution in birefringent fibers. Firstly, the traveling wave transformation is applied to convert the conformable time–space fractional Fokas-Lenells model into two-dimensional planar dynamic system. Secondly, the qualitative analysis of the coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion is discussed by using the plane dynamics system. Moreover, two-dimensional phase portraits, three-dimensional phase portraits, Poincaré sections and sensitivity analysis of its perturbed system are drawn by using the Maple mathematical software. Finally, the optical soliton solutions of the coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion are obtained by using planar dynamical system method.

Pynamical is an educational Python package for introducing the modeling, simulation, and visualization of discrete nonlinear dynamical systems and chaos, focusing on one-dimensional maps (such as the logistic map and the cubic map). Pynamical facilitates defining discrete one-dimensional nonlinear models as Python functions with just-in-time compilation for fast simulation. It comes packaged with the logistic map, the Singer map, and the cubic map predefined. The models may be run with a range of parameter values over a set of time steps, and the resulting numerical output is returned as a pandas DataFrame. Pynamical can then visualize this output in various ways, including with bifurcation diagrams, two-dimensional phase diagrams, three-dimensional phase diagrams, and cobweb plots. These visualizations enable simple qualitative assessments of system behavior including phase transitions, bifurcation points, attractors and limit cycles, basins of attraction, and fractals.

Intradural spinal lipoma (ISL) prevalent in children and young adults usually presents with spastic progressive quadriparesis, sensory disturbances, and gait abnormalities. Chaotic lipomas named due to their haphazard distribution are an extremely rare variant of ISL present at the dorsal root entry zone. We describe a case of chaotic spinal lipoma and elucidate the challenges faced in the management of this entity. [ABSTRACT FROM AUTHOR]

Titanium alloys has significance in engineering applications owing to their enhanced properties and its ability to retain the shape at elevated temperatures. A new Teaching Learning Based Optimization (TLBO) variant was developed with multiple search features to mitigate cutting force and surface irregularities in Titanium samples. This assists to achieve the best quality of the product at minimal cutting energy. Experiments were conducted and the significance of machining parameters on cutting force and surface finish were analyzed. It is ascertained that the best surface is attained at a lower tool feed rate with higher cutting speed. The increase of nose radius has more influence on the surface quality. Chaotic multiobjective TLBO with multiple effective guidance was applied in both single objective and multiobjective optimization, where useful information of other non-fittest learners is leveraged for effective more population search. The performance of the new algorithm was evaluated and comprehensively discussed. The minimum cutting force F z = 65.06 N and R a = 1.41 μ m can be achieved with v = 130 m / m i n , f = 0.051 m m / r e v , nr = 0.4 m m and ap = 0.5 m m. The predicted results were validated experimentally and verified with other existing optimizers. It is concluded that this new algorithm can be applied in machining and production wastage can be greatly minimized. [ABSTRACT FROM AUTHOR]

In this paper, the effect of the bimorph profile on the nonlinear dynamic behavior and performance of a vibratory piezomagnetoelastic energy harvester is investigated. The proposed model is composed of upper and lower piezoelectric layers on a trapezoidal cantilever beam with one attached tip magnet as well as two external magnets. The magnetic field of two external magnets generates magnetic forces and moment on the tip magnet. The bimorph structure is considered as a distributed-parameter system, and the external forces are obtained by analyzing the magnetic field of the external magnets. Equations of motion are obtained using electromagnetic Lagrange equations based on the generalized Hamilton principle and the Euler-Bernoulli beam theory. The proposed model for the bimorph and magnetic forces is validated by previously published experimental results. In order to compare the nonlinear behavior of the rectangular and trapezoidal beam profiles, the bifurcation diagrams are depicted for various control parameters such as the separation distances of the magnets, beam root width, and beam tip width. Verification of the bifurcation diagrams is performed by the phase plane portraits and Poincare maps. Also, the harvested power level is compared for different profiles of the bimorph. Moreover, the simultaneous effects of exciting frequency and bifurcation parameters on the system performance are investigated by the waterfall diagrams. The obtained results show that the trapezoidal beam profile with a lower tip width has higher performance than the rectangular beam. In trapezoidal beam profiles, the subharmonic and chaotic motions have relatively higher output powers than periodic motions.

This work presents the realization of a novel electronically tuneable third-order autonomous chaotic oscillator using a current-controlled current conveyor feedback amplifier (CCCFA). The proposed circuit consists of a single CCCFA, two grounded passive capacitors, one inductor, and two diodes. The chaotic oscillator possesses smooth symmetrical sin-hyperbolic nonlinearity through two antiparallelly connected diodes. The electronically tunable intrinsic resistance at the X terminal serves as the bifurcation control parameter in the circuit and is controlled through bias current. Tuning of bias current enables the formation of different periodic and chaotic attractors. The proposed chaotic oscillator exhibits rich nonlinear dynamical behavior such as periodicity, antimonotonicity, and coexistence of attractors. Multistability is investigated through circuit-level simulation. The chaotic oscillator can easily be implemented in an integrated circuit as the configuration is simple, resistorless, and uses the minimum number of components in the count. Further, a higher dimensional (4D) chaotic oscillator is proposed as an extended circuit of the 3D chaotic oscillator and illustrated as an application in chaos encryption. Simulations are done using TSMC 180nm CMOS technology in PSpice. Experimental results are presented to verify the theoretical and simulation analyses of the proposed circuits.

In recent years, there has been an increasing interest in employing chaotic-based random number generators for cryptographic purposes. However, many of these generators produce sequences that lack the necessary strength for cryptographic systems, such as Tent-Map. However, these generators still suffer from common issues when generating random numbers, including issues related to speed, randomness, lack of statistical properties, and lack of uniformity. Therefore, this paper introduces an efficient pseudo-random number generator, called State-Based Tent-Map (SBTM), based on a modified Tent-Map, which addresses this and other limitations by providing highly robust sequences suitable for cryptographic applications. The proposed generator is specifically designed to generate sequences with exceptional statistical properties and a high degree of security. It utilizes a modified 1D chaotic Tent-Map with enhanced attributes to produce the chaotic sequences. Rigorous randomness testing using the Dieharder test suite confirmed the promising results of the generated keystream bits. The comprehensive evaluation demonstrated that approximately 97.4% of the tests passed successfully, providing further evidence of the SBTM’s capability to produce sequences with sufficient randomness and statistical properties.

In this work, we construct a model of an asymmetrically coupled network of semiconductor chaotic lasers in order to recognize noisy digital images of digits 0–9, derived from different samples in the digital image sets 0–9 found within the MNIST dataset. Here, the lasers network consists of eight asymmetrically coupled semiconductor lasers. The chaotic lasers network is driven by the external inputs, which encode one noise digital image to be recognized. The outputs of the chaotic lasers network driven by a total of 40 samples from the digital image sets 0–9 are utilized as ten sets of reference signals. The output of the chaotic lasers network induced by one noisy digital image is used as a test signal. By judging the maximum of the correlations of the test signal with the ten sets of reference signals, all noisy digital images 0–9 can be recognized well under different noises. Moreover, we further explore the recognition rate for each noisy digital image under different noises and a fixed injection strength. It is found that all noisy digital images can be recognized well under a certain low injection strength. The recognition-rates of all noisy digital images can further decrease to a certain extent under higher noise and a fixed the injection strength. The injection strength has little influence on the recognition rate of one noise digital image target with lower noise. The recognition rate under higher noise maintains a higher value (more than 0.9) when the injection strength is smaller than a certain value, but for the larger injection strength, the recognition rate exhibits further decrease. The modeled chaotic lasers network can play the role of photonic accelerators for the recognition of the noisy digital images.

Highlights: Rock materials exhibit obvious strain rate effects at different loading velocities. The damage evolution process of rock materials contains chaotic features. Logical mapping is used to analyze rock material damage–strain information sequences. The fractal dimension of rock sample crack is positively correlated with load velocity. Rock is a widely used construction material; its mechanical properties change due to the influence of different load speed. In this study, the split Hopkinson pressure bar (SHPB) was used to test the dynamic properties of rock samples by loading four different pressures (0.05, 0.08, 0.14, and 0.23 MPa). The peak stress of the sample increases from 82.19 to 284.16 MPa, and the particle size of the sample debris decreases from 46.57 to 18.34 mm as the impact pressure increases from 0.05 to 0.23 MPa. As a chaos method in nonlinear dynamics, it is introduced into the quantitative evaluation of the sample at four loading pressures, which is then calculated. The damage evolution process of the sample under four loading pressures is calculated, and the chaotic characteristics contained in the process are analyzed. Based on the logistic mapping, the increase in the load velocity can delay the entry of the damage variable into the period-doubling bifurcation and chaotic states. Finally, the fractal dimension of the rock crack at the corresponding time under different load speeds is calculated, and the results showed that the increase in the load velocity can increase the uniformity of the crack distribution. [ABSTRACT FROM AUTHOR]

A novel symmetrical four-wing fourth-order chaotic system is constructed. The basic dynamic characteristics of the system were analyzed by phase diagram, bifurcation diagram, Lyapunov index spectrum, Poincare cross section diagram and 0–1 test. In addition, the chaotic attractors under different parameters in the system are analyzed. In the dynamic analysis of the new system, it is found that the new system has some characteristics, such as multi-stability, offset boosting, multi-state transition phenomenon, transient chaos and intermittent chaos, and coexistence of multiple attractors. These features have the value of in-depth analysis compared to previous systems and can make it promising for more applications. Moreover, after calculating the complexity of the system by C 0 algorithm at different initial values, it is found that the complexity of the system has been stable. Due to the existence of many characteristics, the new chaotic system has attracted great attention. At the same time, the circuit design of the system is realized by using Multisim simulation software and FPGA digital hardware circuit. Finally, a novel and efficient image encryption algorithm is designed by combining multi-direction pixel scrambling and DNA dynamic encryption. The NIST test, key space, encryption histogram, adjacent pixel correlation, robustness and information entropy are analyzed by encrypting images using chaotic sequences of the new system. In a word, its plentiful characteristics and intricate phenomena have significant reference value in the field of chaotic image encryption. • Construct new chaotic system and realize digital hardware circuit. • Dynamic phenomena are abundant. • Image encryption. [ABSTRACT FROM AUTHOR]

In this paper, a new combinatorial structure is introduced for image encryption, which has an excellent encryption effect on security and efficiency. An n-transversal in a Latin square has the function of classifying all the matrix's positions, and it can provide a pair of orthogonal Latin squares. Employing an n-transversal of a Latin square, we can permutate all the pixels of an image group by group for the first time, then use two Latin squares for auxiliary diffusion based on a chaotic sequence, and finally, make use of a pair of orthogonal Latin squares to perform the second scrambling. The whole encryption process is "scrambling–diffusion–scrambling". The experimental results indicated that this algorithm passed various tests and achieved a secure and fast encryption effect, which outperformed many of the latest papers. The final information entropy was very close to 8, and the correlation coefficient was approximately 0. All these tests verified the robustness and practicability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a novel discrete-time (DT) chaotic map-based random-number generator (RNG), namely the Siponi map, which is a modification of the Logistic map. The Logistic map is usually applied to cryptosystems, mainly for the purposes of generating random numbers. In addition to being easy to implement, it has a better security level than other nonlinear functions. However, it can only process positive real-number inputs. Our proposed map is a deterministic function that can process positive and negative real values. We explored the map comprehensively and investigated its characteristics and parameters. We calculated the optimum parameter values using empirical and theoretical mathematical models to yield the maximum randomness of a sequence of bits. The limit variation of the maximum parameter value was determined based on a practical information measure. Empirical verification was performed for the Siponi map to generate bit sequences unrelated to the previous bit with high entropy values, and we found the extractor function threshold value to be 0.5, while the parameter control was −2 or 2. Using our proposed map, a simple RNG without post-processing passed DieHard statistical tests and all the tests on the NIST SP 800-22. Finally, we have implemented a Siponi map-based RNG on the FPGA board and demonstrated that the sources used are LUT = 4086, DSP = 62, and register = 2206. [ABSTRACT FROM AUTHOR]

Feature selection is a critical task for optimizing system performance and reducing computational overhead in the context of Internet of Things (IoT) applications. This paper presents a two-stage feature selection approach specifically designed for IoT scenarios. In the first stage, a variety of feature dimensionality reduction techniques are employed to significantly reduce the dimensionality of the original feature set by more than 50%. This process results in the creation of a highly effective feature subset, which serves as a solid foundation for subsequent feature selection in the second stage. In the second stage, feature selection is performed on the feature subset by an evolutionary algorithm to obtain high accuracy. Notably, we propose an improved whale optimization algorithm (WOA-HA), which incorporates several improvement factors such as a chaotic Hénon map mechanism (HMM), adaptive coefficient vector (ACV), and a binary operator. To assess the effectiveness of our approach, we compare the performance of WOA-HA with other evolutionary algorithms in terms of feature selection outcomes. Through extensive experiments, our proposed approach achieves an average accuracy of up to 95.5% on Aalto IoT dataset and 98.8% on RT-IoT 2022 dataset, respectively. Meanwhile, the average number of selected features reduced by about 82.5% on Aalto IoT dataset and about 62.3% in the RT-IoT 2022 dataset, respectively. Our proposed approach consistently outperforms other methods and achieves the best performance on most datasets with higher accuracy and fewer features. • Two-stage feature selection approach is proposed for the high-dimensionality of IoT data. • A novel WOA-HA algorithm is proposed in the second stage. • WOA-HA has a special chaotic initial solution and adaptive strategy. • The proposed approach outperforms other algorithms on Aalto IoT dataset and RT-IoT 2022 dataset. • The first stage of experimentation with the Aalto dataset resulted in a reduction of the feature set dimensionality by over 50%. [ABSTRACT FROM AUTHOR]

When controlling systems that present chaotic operating zones that produce undesired behavior and the plant is required to present a smooth change when entering this zone, fuzzy controllers have proven to be effective in these types of situations where the only requirement to the design of this is the knowledge of the system and the experience that it has in the control. This project will allow students to consolidate their knowledge in the design of fuzzy controllers and to carry out research with this type of controllers, through a platform made in open software where a license is not required for its use. This platform can design fuzzy controllers and making the fuzzy controller operate autonomously without relying on a computer equipment to perform the tests and commissioning of said plant on a low-cost hardware open board from the Arduino series. [ABSTRACT FROM AUTHOR]

The aim of the experiment is to put online some practical work on the double pendulum by highlighting the chaotic aspect of this system. Then, we experimentally compare the ideal case with the real case (Effect of frictions) and we study the evolution of the system by changing the initial conditions. After having chosen the initial conditions, the learner launches the double pendulum, via the web. Thanks to a fast camera, she/he recovers the video showing the evolution of the system. Then, using a specific pointing software, the positions of the both masses of the double pendulum are detected over time, which allows to compare the real case with the theoretical case (without friction) and therefore to see the friction effect. The purpose of this paper is to carry out remote physics experiments for students to handle and control in real time. The experiment adopted for this work is the double pendulum. It consists of a pendulum attached to the end of another pendulum. The assembly is then set in motion from a configuration, determined by the initial conditions. To conduct this experiment remotely, we proceeded as follows: First of all, the mechanical part, in which we made the 3D design and the simulation using Solidworks in order to validate the design, then, we chose the electronic components that are compatible with the mechanical part. Finally, the IT part for the on-line setting. [ABSTRACT FROM AUTHOR]