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This paper proposes an innovative image encryption algorithm designed for the secondary user system, aiming to break through the single privilege restriction of traditional encryption methods and significantly improve the protection of image data in highly sensitive fields such as military defence and medical health. By introducing hierarchical access control, the algorithm ensures that users with different privileges can only access image information within the authorized range, realizing refined and hierarchical security protection. Meanwhile, the innovative fusion of Tent map and Logistic map constructs a complex and unpredictable delayed perturbation model, which dramatically improves the complexity and randomness of chaotic behaviors and enhances the algorithm security. In addition, the algorithm is highly flexible and can effectively adapt to irregular image structures, ensuring that the encryption process is both efficient and secure. Experimental validation shows that the algorithm performs well in preventing unauthorized access and provides solid security for the storage and transmission of sensitive image information. [ABSTRACT FROM AUTHOR]

At present, there is a growing emphasis on safeguarding image data, yet conventional encryption methods are full of numerous limitations. In order to tackle the limitations of conventional color image encryption methodologies, such as inefficiency and insufficient security, this paper designs an expedited encryption method for color images that uses DNA coding in conjunction with multiple chaotic systems. The encryption algorithm proposed in this paper is based on three-dimensional permutation, global scrambling, one-dimensional diffusion and DNA coding. First of all, the encryption algorithm uses three-dimensional permutation algorithms to scramble the image, which disrupts the high correlation among the image pixels. Second, the RSA algorithm and the SHA-256 hashing algorithm are utilized to derive the starting value necessary for the chaotic system to produce the key. Third, the image is encrypted by using global scrambling and one-dimensional diffusion. Finally, DNA coding rules are used to perform DNA computing. The experimental results indicate that the encryption scheme exhibits a relatively weak inter-pixel correlation, uniform histogram distribution, and an information entropy value approaching eight. This shows that the proposed algorithm is able to protect the image safely and efficiently. [ABSTRACT FROM AUTHOR]

In this paper, we put forward a novel hyperchaotic image encryption method using machine learning-RBF. First, a new 4D continuous hyperchaotic system is designed to address the degradation issue of low-dimensional continuous chaotic systems, which has a simpler structure, wider chaotic range, better distribution, and higher complexity compared with other chaotic systems based on Hopfield-type neural networks. Additionally, it has good randomness and can be implemented using hardware-based digital signal processing. Then, based on this system, we explore a new image encryption method using machine learning-radial basis function (RBF) neural network and true random numbers. Results show that compared with some other algorithms, our method is more secure and withstand common attacks. [ABSTRACT FROM AUTHOR]

Discrete-time chaotic systems exhibit nonlinear and unpredictable dynamic behavior, making them very difficult to classify. They have dynamic properties such as the stability of equilibrium points, symmetric behaviors, and a transition to chaos. This study aims to classify the time series images of discrete-time chaotic systems by integrating deep learning methods and classification algorithms. The most important innovation of this study is the use of a unique dataset created using the time series of discrete-time chaotic systems. In this context, a large and unique dataset representing various dynamic behaviors was created for nine discrete-time chaotic systems using different initial conditions, control parameters, and iteration numbers. The dataset was based on existing chaotic system solutions in the literature, but the classification of the images representing the different dynamic structures of these systems was much more complex than ordinary image datasets due to their nonlinear and unpredictable nature. Although there are studies in the literature on the classification of continuous-time chaotic systems, no studies have been found on the classification of discrete-time chaotic systems. The obtained time series images were classified with deep learning models such as DenseNet121, VGG16, VGG19, InceptionV3, MobileNetV2, and Xception. In addition, these models were integrated with classification algorithms such as XGBOOST, k-NN, SVM, and RF, providing a methodological innovation. As the best result, a 95.76% accuracy rate was obtained with the DenseNet121 model and XGBOOST algorithm. This study takes the use of deep learning methods with the graphical representations of chaotic time series to an advanced level and provides a powerful tool for the classification of these systems. In this respect, classifying the dynamic structures of chaotic systems offers an important innovation in adapting deep learning models to complex datasets. The findings are thought to provide new perspectives for future research and further advance deep learning and chaotic system studies. [ABSTRACT FROM AUTHOR]

Mathematical models such as Fitzhugh–Nagoma and Hodgkin–Huxley models have been used to understand complex nervous systems. Still, due to their complexity, these models have made it challenging to analyze neural function. The discrete Rulkov model allows the analysis of neural function to facilitate the investigation of neuronal dynamics or others. This paper introduces a fractional memristor Rulkov neuron model and analyzes its dynamic effects, investigating how to improve neuron models by combining discrete memristors and fractional derivatives. These improvements include the more accurate generation of heritable properties compared to full-order models, the treatment of dynamic firing activity at multiple time scales for a single neuron, and the better performance of firing frequency responses in fractional designs compared to integer models. Initially, we combined a Rulkov neuron model with a memristor and evaluated all system parameters using bifurcation diagrams and the 0–1 chaos test. Subsequently, we applied a discrete fractional-order approach to the Rulkov memristor map. We investigated the impact of all parameters and the fractional order on the model and observed that the system exhibited various behaviors, including tonic firing, periodic firing, and chaotic firing. We also found that the more I tend towards the correct order, the more chaotic modes in the range of parameters. Following this, we coupled the proposed model with a similar one and assessed how the fractional order influences synchronization. Our results demonstrated that the fractional order significantly improves synchronization. The results of this research emphasize that the combination of memristor and discrete neurons provides an effective tool for modeling and estimating biophysical effects in neurons and artificial neural networks. [ABSTRACT FROM AUTHOR]

NETmix is a network of mixing chambers interconnected by channels, in which the most efficient mixing occurs under chaotic flow regimes. Chaos is highly influenced by the topology, particularly by the ratio chamber diameter/channel width, D/d. In this work, micromixing in NETmix is characterized through Lagrangian Mixing Simulation (LMS), which enables to establish the relation between the degree of mixing and the topology, D/d. The degree of mixing is then related with the Eulerian chaoticity from hydrodynamics and spectral analysis. The best mixing is obtained at D/d = 6.65 and is associated to a thin 8 shaped strange attractor. The spectral analysis shows a principal oscillation frequency at St = 0.13. Since the quasi‐periodic regime is alternated with chaotic behavior, NETmix has an intermittent bifurcation. For the NETmix system, orderly flows in the quasi‐periodic regime have higher mixing intensity than less orderly flows in the weak or strong chaotic regimes. [ABSTRACT FROM AUTHOR]

Machine learning methods based on reservoir computing have shown great potential in predicting the dynamics of complex systems. However, the learning and prediction processes of the reservoir are often considered as a 'black box', whose mechanism is unknown. As the first step to explore its mechanism and dynamical features, characterizing the learning capability of the reservoir is of great significance in practice and one of the key problems in the theoretical study of reservoir computing. In this paper we explore the learning capacity of reservoir computing with polynomial functions, and find a universal error stairs independent of the input signals. Based on the error stairs, we propose two indicators to characterize the learning capability of the reservoir with noise signals as input, the highest degree polynomial error and the memory length, for the nonlinear processing ability and memory ability of reservoirs respectively. These two indicators provide a method to choose the hyper-parameters of reservoir computing. We validate and apply these two indicators through predictions on classical chaotic systems such as the logistic map and the Lorenz system. These two indicators provide a promising tool to study the learning capacity of reservoir computing and other machine learning method for dynamical systems. [ABSTRACT FROM AUTHOR]

One of several system classes that are frequently encountered in nonlinear and chaos control theory and its applications is the strict feedback form. The dynamics of many nonlinear and chaotic systems can be transformed into the strict feedback form via a change of variables as well. In this paper, a new discrete-time adaptive nonlinear controller is examined for a class of discrete-time high-order nonlinear systems in strict-feedback form. The proposed controller structure consists of a discrete-time controller built on a Lyapunov function, including a positive semi-definite function, and an adaptation mechanism that estimates unknown time-invariant parameters. The contributions of the proposed discrete-time method are twofold. One is that the discrete-time strict-feedback nonlinear systems are re-evaluated by a transformation, which enables us to design a flexible discrete-time controller. An elegant adaptive nonlinear controller is constructed without the complicated design steps, which is one of the main drawbacks encountered in controller design for general strict-feedback nonlinear systems. Owing to the mentioned transformation, computational complexity associated with other examples in the literature is effectively tackled and reduced. Another is that conventional least squares estimation is employed, demonstrating that the closed-loop error dynamics converge to the origin in an uncertain discrete-time internal model. Simulation results on two discrete-time nonlinear systems and a chaotic system verify the contributions of the proposed method. [ABSTRACT FROM AUTHOR]

In this research work, we investigate a new three-dimensional jerk system with three parameters in which one of the nonlinear terms is a sinusoidal nonlinearity. We show that the new jerk system has two unstable equilibrium points on the ��-axis. Numerical integrations show the existence of periodic and chaotic states, as well as unbounded solutions. Consideration of the Poincaré sphere at infinity found no periodic states. We show that the new jerk system exhibits multistability with coexisting attractors. We also present results for the offset boosting of the proposed chaotic jerk system. Using MultiSim version 14.1, we design an electronic circuit for the new jerk system with a sinusoidal nonlinearity. As a control application, we design complete synchronization for the master-slave jerk systems using backstepping control technique. Simulations are presented to illustrate the main results of this research work.

In this paper, we present the design, development, and pilot implementation of a Teaching–Learning Sequence (TLS) about the physics of deterministic chaos. The main aim of the activities is to let students become aware of two key ideas about deterministic chaos: (1) the role of initial conditions and (2) the graphical representation in a momentum–position graph. To do so, the TLS is based on the observation and analysis of the trajectory of the free end of a double pendulum through the modeling software Tracker. In particular, the Tracker-based activities help students understand that, by modifying the well-known simple pendulum dynamic system into a double pendulum, long-time-scale predictability is lost, and a completely new behavior appears. The TLS was pilot tested in a remote teaching setting with about 70 Italian high school students (16–17 years old). The pretest analysis shows that before participating in the activities, students held typical misconceptions about chaotic behavior. Analysis of the written responses collected during and after implementation shows that the proposed activities allowed students to grasp the two key ideas about nondeterministic chaos. A possible integration of the TLS with an online simulation is finally discussed. [ABSTRACT FROM AUTHOR]

In recent years, memristors have received widespread attention due to their inherent nonlinear characteristics. To this end, a three-dimensional memristor chaotic system based on secondary nonlinear magnetron memristors has been constructed. Through the analysis of phase portraits, 0–1 tests, Poincare sections, bifurcation diagrams, and Lyapunov exponent spectra, it was found that the system exhibits rich dynamical behaviors, including immovable points, periodic orbits, and chaos. The coexistence attractors of the system were studied, and their basins were also plotted. Comparative complexity analysis indicates that the chaotic system possesses high complexity, thus providing higher security for image encryption. The practicality of the chaotic system was verified through circuit simulation and FPGA. Finally, the chaotic system was applied to DNA image encryption. The focus was on analyzing the histogram, adjacent pixel correlation, information entropy, security, and runtime. The analysis results demonstrate that the algorithm has high security and practicality. [ABSTRACT FROM AUTHOR]

The present work presents the investigation of the dynamics and influence of chaotic behavior on energy capture for a U-shaped structure (portal frame) that contains shape memory alloy (SMA), piezoelectric material (PZT), a nonlinear energy sink (NES) and a non-ideal excitation source represented by an unbalanced electric motor coupled to the U-structure. The mathematical model presents nonlinearities arising from the nonlinear stiffness of the U-structure, the NES system, the SMA, and the PZT material. Chaotic behavior is assessed through time history, bifurcation diagrams, phase diagrams, and the 0–1 test. Energy capture is carried out through a piezoelectric material (PZT), represented by a non-linear electromechanical coupling model, and electromagnetic induction generated by the non-linear electromagnetic energy sink coupled to the structure (NES). Dynamic analysis is performed through parametric analysis of parameters related to piezoelectric coupling and NES parameters. Numerical simulations demonstrate that the system has chaotic behavior for specific parameters and that its energy capture is influenced by parametric variation. It is shown numerically that the parameters of the SMA material, the PZT material, and the NES significantly influence the chaotic behavior and energy capture of the investigated electromechanical system. [ABSTRACT FROM AUTHOR]

To enhance the security of image data, this paper proposes a quantum-classical hybrid image encryption scheme based on parameterized pixel ratios. The scheme utilizes the pixel ratio of the image as parameters for quantum walks, Henon mapping, and Arnold Cat mapping, approximating the "one-time pad" encryption effect. With this scheme, even when encrypting multiple images using the same parameters, the resulting quantum walks random matrix and chaotic system trajectories are almost completely different. This encryption scheme eliminates the need for quantum representation of the image, thereby conserving quantum resources and reducing implementation complexity. Experimental results show that the scheme can resist statistical analysis, key analysis, noise and occlusion attacks, and has strong key sensitivity and large key space. Compared to other encryption schemes, the proposed approach exhibits advantages in terms of information entropy and plaintext sensitivity, indicating its higher level of security. [ABSTRACT FROM AUTHOR]

This manuscript introduces a piecewise linear decomposition method devoted to a class of fractional-order dynamical systems composed of piecewise linear (PWL) functions. Inspired by the Adomian decomposition method, the proposed technique computes an approximated solution of fractional-order PWL systems using only linear operators and specific constants vectors for each sub-domain of the PWL functions, with no need for the Adomian polynomials. The proposed decomposition method can be applied to fractional-order PWL systems composed of nth PWL functions, where each PWL function may have any number of affine segments. In particular, we demonstrate various examples of how to solve fractional-order systems with 1D 2-scroll, 4-scroll, and 4 × 4 -grid scroll chaotic attractors by applying the proposed approach. From the theoretical and implementation results, we found the proposed approach eliminates the unneeded terms, has a low computational cost, and permits a straightforward physical implementation of multi-scroll chaotic attractors on ARMs and FPGAs digital platforms. [ABSTRACT FROM AUTHOR]

Encryption of images is an important method that can effectively improve the security and privacy of crucial image data. Existing methods generally encrypt an image with a combination of scrambling and encoding operations. Currently, many applications require highly secure results for image encryption. New methods that can achieve improved randomness for both the scrambling and encoding processes in encryption are thus needed to further enhance the security of a cipher image. This paper proposes a new method that can securely encrypt color images. As the first step of the proposed method, a complete bit-level operation is utilized to scramble the binary bits in a color image to a full extent. For the second step, the bits in the scrambled image are processed with a sweeping operation to improve the encryption security. In the final step of encryption, a codebook that varies with evolutionary operations based on several chaotic systems is utilized to encrypt the partially encrypted image obtained in the second step. Experimental results on benchmark color images suggest that this new approach can securely encrypt color images and generate cipher images that remain secure under different types of attacks. The proposed approach is compared with several other state-of-the-art encryption approaches and the results show that it can achieve improved encryption security for cipher images. Experimental results thus suggest that this new approach can possibly be utilized practically in applications where color images need to be encrypted for content protection. [ABSTRACT FROM AUTHOR]

Aiming at the problems of weak security and susceptibility to violent cracking in traditional image encryption algorithms, this paper presents a novel image encryption algorithm based on the Coyote Optimization Algorithm (COA) and the hyperchaotic Lorenz system. The hyperchaotic Lorenz system exhibits sensitivity to both initial conditions and parameters, and complex dynamics behavior. These characteristics pose a challenge for attackers attempting to extract essential information from the image through analysis, thereby enhancing the algorithm's resistance to cracking. Nevertheless, the hyperchaotic Lorenz system is susceptible to the initial values of state variables, and its initial parameters can be easily deciphered. Consequently, this study suggests employing the COA to optimize the sequence generated by the chaotic system. This is done to increase the randomness and complexity of the key, making it more challenging to crack. Given that COA gets trapped in local optima when dealing with high-dimensional problems, this paper proposes the Lévy-flight Coyote Optimization Algorithm (LCOA). By implementing the LCOA, which involves larger step sizes and faster jumps, the algorithm is expected to achieve global optimality during the optimization search process. The experimental results demonstrate that the optimization results of the generated sequence of the hyperchaotic Lorenz system by LCOA can eliminate patterns and regularities of pixel points in the image generated effectively. This leads to a significant enhancement in the resistance of the image encryption algorithm to differential attacks, resulting in a significant enhancement in image encryption performance. [ABSTRACT FROM AUTHOR]

Chaotic systems are highly sensitive to initial conditions, meaning small changes can lead to significant outcomes. This sensitivity can be leveraged to enhance the flexibility and adaptability of supply chains, allowing them to respond quickly to changing market demands and conditions. In this research work, we obtain a New Chaotic Supply Chain Model (NCSCM) by introducing a sinusoidal model uncertainty in the third differential equation of the Hamidzadeh chaotic supply chain model (2023). The sinusoidal uncertainty in the model accounts for the volatility and fluctuations of the supply chain model. We investigate the dynamic behaviors of NCSCM by performing a detailed Bifurcation Diagram (BD) analysis and Lyapunov Exponents (LEs). Next, we carry out a 0−1 test for the NCSCM to confirm the chaotic attractor of the system. We also study the multi-stability properties of the NCSCM. Finally, with the help of backstepping control, we derive new results for the complete synchronization of the novel chaotic supply chain models.

Objective: In this article, time-varying chaotic systems with uncertainties, including external disturbances, are considered, and sliding mode control (SMC) is used to control such systems. To control these systems, an autonomous differential equation is first introduced. Then, based on this differential equation, a sliding surface is defined to control this chaotic system. This kind of controller is remarkable in that it removes the effects of disturbances, whether bounded or unbounded. Therefore, the system is known to be fixed-time stable. where the trajectories of this chaotic system are not placed on the sliding surface, we have created creative controllers to place the trajectories on the sliding surface in finite time. Theoretical investigations show that such chaotic systems can be made fixed-time stable by applying the controls proposed in this study. Based on the findings of this study, the controllers are designed to eliminate all disturbances, whether bounded or unbounded. the results be said to apply chaotic, time-dependent, and time-independent systems. To further consolidate the results obtained in this article, two examples, namely the time-dependent system of the Gyro and the time-independent system of the Liu, are investigated, and the results were compared with previous works by other researchers.

Based on the fractional calculus and sliding mode control (SMC) techniques, this paper presents a predefined-time synchronization scheme for fractionalorder chaotic systems (FOCSs). Firstly, a predefined-time control method is proposed for fractional-order systems. Subsequently, a novel sliding surface is presented to ensure predefined-time convergence of the synchronization error. Then, a controller is designed by combining the predefined-time stability and the SMC method to ensure that the synchronization error converges to zero within the predefined time. Finally, the feasibility and robustness of the scheme are illustrated with two numerical simulation examples. [ABSTRACT FROM AUTHOR]

Smartphones, digital cameras, and other imaging devices generate vast amounts of high-resolution colored images daily, stored on devices equipped with multi-core central processing units or on the cloud. Safeguarding these images from potential attackers has become a pressing concern. This paper introduces a set of six innovative image ciphers designed to be stronger, faster, and more efficient. Three of these algorithms incorporate the State-Based Tent Map (SBTM) Chaotic Pseudo Random Number Generator (CPRNG), while the remaining three employ a proposed modified variant, SBTMPi. The Grayscale Image Cipher (GIC), Colored Image Cipher Single-Thread RGB (CIC1), and Colored Image Cipher Three-Thread RGB (CIC3) showcase the application of the proposed algorithms. By incorporating novel techniques in the confusion and diffusion phases, these ciphers demonstrate remarkable performance, particularly with large colored images. The study underscores the potential of SBTM-based image ciphers, contributing to the advancement of secure image encryption techniques with robust random number generation capabilities. [ABSTRACT FROM AUTHOR]

While increasingly complex algorithms are being developed for graph classification in highly-structured domains, such as image processing and climate forecasting, they often lead to over-fitting and inefficiency when applied to human interaction networks where the confluence of cooperation, conflict, and evolutionary pressures produces chaotic environments. We propose a graph transformation approach for efficient classification in chaotic human systems that is based on game theoretic, network theoretic, and chaos theoretic principles. Graph structural properties are compiled into time-series that are then transposed into the frequency domain to offer a dynamic view of the system for classification. We propose a set of benchmark data sets and show through experiments that the approach is efficient and appropriate for many dynamic networks in which agents both compete and cooperate, such as social media networks, stock markets, political campaigns, legislation, and geopolitical events. [ABSTRACT FROM AUTHOR]

This paper proposes a user-biometric-based image encryption using chaotic dynamical systems, SHA-256 hash function, and zigzag transformation. Three chaotic systems, namely, the Henon map, logistic map, and Lorenz system, are used to apply the chaotic properties to the encryption system. The hash value of the user biometric image is used to generate the initial value of the Henon map. The initial values for the logistic map and Lorenz system are generated from the hash value of the plain image. SHA-256 hash algorithm generates the hash values of the biometric and plain images. The plain image is scrambled using the two-dimensional chaotic values generated by the Henon map first. Next, the first scrambled image's pixels are XORed with the one-dimensional chaotic values generated from the logistic map and produce the second scrambled image. Finally, take the second scrambled image's pixels, and XOR them with the three-dimensional chaotic values generated from the Lorenz system and create the final encrypted image. The robustness and flexibility of the encryption system are analyzed using various security and performance analyses. The experiment results are compared with the existing algorithms to prove the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we have extended the concept of advanced Julia function for the discovery of new type of trajectories existing inside outer and inner wings. A dynamical system based on four rotors, referred to as quadrotor unmanned aerial vehicle (QUAV), is considered for the first time to seek the generation of extra wings using fractal theory. Moreover, we have used Julia and advanced Julia function techniques for the creation of outer and inner wings, respectively. Furthermore, the trajectories achieved using both techniques are analyzed and compared with the aid of basin of attraction and bifurcation diagram. This work covers a gap in the literature, that what is the impact of global dynamics on the hidden fractals. Therefore to fill this gap, sets of initial points are plotted from each basin constructed for fractals-based QUAV systems. Finally, numerical simulations are carried out using MATLAB, whereas the data generated for the corresponding basins are attached for the convenience of readers to reproduce each figure. [ABSTRACT FROM AUTHOR]

In this research work, we investigate a new three-dimensional jerk system with three parameters in which one of the nonlinear terms is a sinusoidal nonlinearity. We show that the new jerk system has two unstable equilibrium points on the x-axis. Numerical integrations show the existence of periodic and chaotic states, as well as unbounded solutions. Consideration of the Poincaré sphere at infinity found no periodic states. We show that the new jerk system exhibits multistability with coexisting attractors. We also present results for the offset boosting of the proposed chaotic jerk system. Using MultiSim version 14.1, we design an electronic circuit for the new jerk system with a sinusoidal nonlinearity. As a control application, we design complete synchronization for the master-slave jerk systems using backstepping control technique. Simulations are presented to illustrate the main results of this research work. [ABSTRACT FROM AUTHOR]

This paper studies the synchronization and control of chaotic systems while proposing a novel chaotic-based path-tracking application for mobile robots (MRs) to ensure their safety and security. In security-based applications that use MRs, such as patrol MRs, the path of the MRs must be complex enough to prevent easy prediction. Multiple chaotic systems with a chaotic switching mechanism are introduced for secure path planning. The main challenges are that the dynamics of MRs are entirely unknown. The modeled dynamics of the MRs are unreliable in practice due to a broad range of uncertainties related to the parameters, operating conditions, environmental impacts, time delays, unmodeled frictions, noisy sensors, and faulty actuators. Also, the chaotic switching of reference signals between chaotic signals imposes a high dynamic perturbation. The main novelties are as follows: (1) a strong secure path is introduced for MRs. (2) A powerful fractional-order predictive controller using type-3 (T3) fuzzy-logic systems (FLSs) is developed. (3) The estimation and prediction errors of T3-FLSs are compensated by a designed parallel compensator. (4) T3-FLSs are tuned online, such that stability is ensured, and prediction accuracy is guaranteed. (5) The suggested scheme is implemented on a real-world MR, and the results demonstrate the feasibility and accuracy of the proposed method. Also, in several simulations, the efficacy of the introduced controller is examined. [ABSTRACT FROM AUTHOR]

Multistep prediction of high-dimensional time series is an essential and challenging task. In this study, we propose an integrated reservoir predictor for making accurate and robust multistep-ahead forecasts based on short-term high-dimensional time series. Initially, a conjugated pair of Spatiotemporal Information (STI) equations is derived using Takens' embedding theory to transform the spatial information of high-dimensional variables into one-dimensional temporal information of the target variable and vice versa. Next, by exploiting reservoir networks, reservoir-based STI equations are established to efficiently capture nonlinear dynamics of the target system with only linear optimization. Then, through an integration phase, the integrated reservoir predictor can output precise and robust predictions of the multistep-ahead states of any target variable. The integrated reservoir predictor outperforms some other prediction methods (including reservoir computing, long-short-term-memory network, convolutional neural network and support vector regression), when applied to classical dynamic systems (e.g. 60D double scroll model, 40D Lorenz 96 model, and 60D Rössler model) and real-world datasets (solar generation data and PM2.5 concentration records), as indicated by evaluation metrics such as Pearson correlation coefficients exceeding 0.9 and root-mean-square errors below 0.3, even in the presence of noise in training data. [ABSTRACT FROM AUTHOR]

Existing biohashing authentication schemes usually store bioinformation in the cloud, whose storage method can face the problems of bioinformation leakage and tampering, and single point of failure. To address the above problems, a ciphertext speech biohashing authentication scheme based on chaotic system and improved public chain is proposed. First, the fusion features are extracted and generated with the inner product of 3D chaotic system to generate the biohashing sequence. Second, the original speech is encrypted and uploaded to the InterPlanetary file system and then, uploaded to the blockchain after the data are encrypted. Finally, the server matches the hash sequence queried on the chain with the to-be-authenticated hash at the user's end using the Hamming distance. The experimental results show that the biohashing algorithm in this paper has better distinguishability, robustness, security and time efficiency. The key space of the speech encryption algorithm is 2 256 , which can well resist the exhaustive attack and ensure the security during speech authentication. In this paper, the combination of on-chain and off-chain storage of speech information can prevent the problem of bioinformation leakage and tampering, as well as avoiding the problem of single point of failure. [ABSTRACT FROM AUTHOR]

The present study investigates unsteady wake dynamics in flow past an oscillating cylinder. A two-dimensional computational analysis is undertaken for flow past a sinusoidally oscillating cylinder. Operating parameters like Reynolds number, forcing frequency, amplitude, and wavelength are systematically varied, and their effect on wake dynamics is investigated. Lift and drag coefficients are plotted with cylinder position to characterize the flow. The flow field is analyzed using Proper Orthogonal Decomposition (POD). POD mode shapes and Power Spectral Density (PSD) plots characterize the flow response to cylinder oscillations. The effect of frequency ratio is examined in achieving synchronized vortex shedding. Previous studies focus on two extremes- the cylinder is either stationary or oscillating with perfect phase-locking. Flow past an oscillating cylinder where Karman and forcing frequencies compete for dominance is rarely reported. This paper considers such a scenario and demonstrates how POD can identify coherent structures, their significance, and associated frequencies. Further, non-symmetric vortex shedding, which is not a common observation, is captured and discussed. Large amplitude and large wavelength regimes are investigated, which remained unexplored in previous research. Coherent structures associated with those regimes are identified. [ABSTRACT FROM AUTHOR]

Predicting time series, especially those originating from chaotic and nonlinear dynamic systems, is a critical research area with broad applications across various fields. Neural networks and fuzzy systems have emerged as leading methods for forecasting chaotic time series. This study introduces an improved adaptive neural-fuzzy inference system (ANFIS) specifically tailored for forecasting chaotic time series. Unlike traditional ANFIS models, which are primarily designed for static problems, this enhanced version incorporates self-feedback relationships from previous outputs to capture the time dependencies inherent in dynamic systems. Additionally, a hybrid approach combining the Imperialist Competitive Optimization Algorithm (ICA) and Least Squares Estimation (LSE) is employed to train the neural-fuzzy system and update its parameters. This method circumvents challenges associated with training gradient-based algorithms. The proposed technique is applied to predict and model multiple nonlinear and chaotic time series from realworld scenarios. Comparative analyses with recent works demonstrate the superior performance of the proposed method, particularly in terms of the prediction total error criterion for time series modeling and forecasting. These results highlight the effectiveness of incorporating self-feedback relationships and utilizing the CCA-LSE hybrid approach in enhancing the predictive capabilities of adaptive neural-fuzzy inference systems for chaotic time series. [ABSTRACT FROM AUTHOR]

In the recent years, significant research interest has been devoted in the modelling and applications of chaotic systems with stable equilibria. In this research study, we propose a new 3-D chaotic system with two stable node-foci equilibria and an unstable saddle-focus equilibrium. We conduct a detailed bifurcation analysis for the new chaotic system with the aid of bifurcation diagrams and Lyapunov exponents. We also show that the new chaotic system has multistability with coexisting attractors. Using MultiSim version 14.1, we design an electronic circuit for the proposed 3-D chaotic system. Finally, as an application, we introduce a voice cryptosystem using the new chaotic system with two stable node-foci equilibrium points and an unstable saddle-focus equilibrium point and its hardware realization on the FPGA platform.

The swift development of the Internet of Things (IoT) has accelerated digitalization across several industries, offering networked applications in fields such as security, home automation, logistics, and quality control. The growth of connected devices, on the other hand, raises worries about data breaches and security hazards. Because of IoT devices’ computational and energy limits, traditional cryptographic methods face issues. In this context, we emphasize the importance of our contribution to image encryption in IoT environments through the proposal of Multiple Map Chaos Based Image Encryption (MMCBIE), a novel method that leverages the power of multiple chaotic maps. MMCBIE uses multiple chaotic maps to construct a strong encryption framework that considers the inherent features of digital images. Our proposed method, MMCBIE, distinguishes itself by integrating multiple chaotic maps like Henon Chaotic Transform and 2D-Logistic Chaotic Transform in a novel combination, a unique approach that sets it apart from existing schemes. Compared to other chaotic-based encryption systems, this feature renders them practically indistinguishable from pure visual noise. Security evaluations and cryptanalysis confirm MMCBIE’s high-level security properties, indicating its superiority over existing image encryption techniques. MMCBIE demonstrated superior performance with NPCR (Number of Pixel Changing Rate) score of 99.603, UACI (Unified Average Changing Intensity) score of 32.8828, MSE (Mean Square Error) score of 6625.4198, RMSE (Root Mean Square Error) score of 80.0063, PSNR (Peak Signal to Noise Ratio) score of 10.2114, and other security analyses.

We propose a double image encryption scheme combining DNA, parallel compressed sensing, enhanced Zigzag confusion, chaotic sparse basis matrix, and chaotic permutation. Firstly, use the logistic map to scramble a Discrete Wavelet Transformation (DWT) matrix to obtain a chaotic DWT matrix. Next, 2D-LICM generates the measurement matrix. Parallel compressed sensing is then performed separately on the two images. Then, enhanced Zigzag confusion and DNA encryption are performed on the new matrix using chaotic sequences to obtain an encrypted image. The chaotic system’s initial value is generated using SHA-256, which has a strong sensitivity to the plain image. We improve on the third-order Colpitts chaotic circuit to construct a more general higher-order Colpitts chaotic oscillator and propose a new fourth-order Colpitts chaotic system. The performance analysis indicates that our encryption algorithm provides excellent security and performance while saving storage space.

A hyperjerk system pertains to a dynamical system regulated by an ordinary differential equation of $n$ th order, where $n \geq 4$ . The main contribution of this work is the finding of a new autonomous hyperjerk system with a half line equilibrium. The mathematical framework of the proposed hyperjerk system contains eight terms with an absolute function nonlinearity. The essential dynamic characteristics of the model are explored, encompassing analysis of equilibrium points and their stability, depiction of the phase trajectories, illustration of bifurcation patterns, and visualization of Lyapunov exponent graphs. Our finding shows that the new 4D hyperjerk system exhibits special behavior like multistability, period doubling reversals and antimonotonocity. The proposed hyperjerk system has been implemented with an electronic circuit using MultiSim 14.0. Moreover, the FPGA implementation of the proposed hyperjerk system is performed by applying two numerical methods: Forward Euler and Trapezoidal. Experimental attractors are given from an oscilloscope by using the Zybo Z7-20 FPGA development board, which are in good agreement with the MATLAB and MultiSim 14.0 simulations. Finally, based on the chaotic dynamical behavior of the proposed chaotic hyperjerk system, a new image encryption approach is proposed. The experimental outcomes of the presented encryption algorithm prove its efficiency and security.

The use of wheeled mobile robots (MRs) with symmetrical structure in engineering is rapidly increasing, with applications in various fields, such as industry, agriculture, forestry, healthcare, mining, rehabilitation, search and rescue, household tasks, remote locations, and entertainment. As MRs become more common, researchers are focusing on developing better ways to model and control these robots to improve their performance and adaptability. The main challenges in this area include uncertain dynamics, non-holonomic constraints, and various perturbations, which complicate the design of the control system. This paper presents a new predictive control scheme for MRs that is independent of the dynamics and the robot’s working environment. A Type-3 fuzzy logic system is developed to identify the MR dynamics online. The designed predictive scheme improves accuracy and speeds up convergence, while also addressing uncertainties and considering constraints on control input. Additionally, a chaotic-based system is proposed for secure path planning, generating a complex and unpredictable reference trajectory that is useful for patrol MR applications. The effectiveness of the suggested controller is demonstrated through simulations and experiments.

In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.

At present, there is a growing emphasis on safeguarding image data, yet conventional encryption methods are full of numerous limitations. In order to tackle the limitations of conventional color image encryption methodologies, such as inefficiency and insufficient security, this paper designs an expedited encryption method for color images that uses DNA coding in conjunction with multiple chaotic systems. The encryption algorithm proposed in this paper is based on three-dimensional permutation, global scrambling, one-dimensional diffusion and DNA coding. First of all, the encryption algorithm uses three-dimensional permutation algorithms to scramble the image, which disrupts the high correlation among the image pixels. Second, the RSA algorithm and the SHA-256 hashing algorithm are utilized to derive the starting value necessary for the chaotic system to produce the key. Third, the image is encrypted by using global scrambling and one-dimensional diffusion. Finally, DNA coding rules are used to perform DNA computing. The experimental results indicate that the encryption scheme exhibits a relatively weak inter-pixel correlation, uniform histogram distribution, and an information entropy value approaching eight. This shows that the proposed algorithm is able to protect the image safely and efficiently.

Discrete-time chaotic systems exhibit nonlinear and unpredictable dynamic behavior, making them very difficult to classify. They have dynamic properties such as the stability of equilibrium points, symmetric behaviors, and a transition to chaos. This study aims to classify the time series images of discrete-time chaotic systems by integrating deep learning methods and classification algorithms. The most important innovation of this study is the use of a unique dataset created using the time series of discrete-time chaotic systems. In this context, a large and unique dataset representing various dynamic behaviors was created for nine discrete-time chaotic systems using different initial conditions, control parameters, and iteration numbers. The dataset was based on existing chaotic system solutions in the literature, but the classification of the images representing the different dynamic structures of these systems was much more complex than ordinary image datasets due to their nonlinear and unpredictable nature. Although there are studies in the literature on the classification of continuous-time chaotic systems, no studies have been found on the classification of discrete-time chaotic systems. The obtained time series images were classified with deep learning models such as DenseNet121, VGG16, VGG19, InceptionV3, MobileNetV2, and Xception. In addition, these models were integrated with classification algorithms such as XGBOOST, k-NN, SVM, and RF, providing a methodological innovation. As the best result, a 95.76% accuracy rate was obtained with the DenseNet121 model and XGBOOST algorithm. This study takes the use of deep learning methods with the graphical representations of chaotic time series to an advanced level and provides a powerful tool for the classification of these systems. In this respect, classifying the dynamic structures of chaotic systems offers an important innovation in adapting deep learning models to complex datasets. The findings are thought to provide new perspectives for future research and further advance deep learning and chaotic system studies.

Mathematical models such as Fitzhugh–Nagoma and Hodgkin–Huxley models have been used to understand complex nervous systems. Still, due to their complexity, these models have made it challenging to analyze neural function. The discrete Rulkov model allows the analysis of neural function to facilitate the investigation of neuronal dynamics or others. This paper introduces a fractional memristor Rulkov neuron model and analyzes its dynamic effects, investigating how to improve neuron models by combining discrete memristors and fractional derivatives. These improvements include the more accurate generation of heritable properties compared to full-order models, the treatment of dynamic firing activity at multiple time scales for a single neuron, and the better performance of firing frequency responses in fractional designs compared to integer models. Initially, we combined a Rulkov neuron model with a memristor and evaluated all system parameters using bifurcation diagrams and the 0–1 chaos test. Subsequently, we applied a discrete fractional-order approach to the Rulkov memristor map. We investigated the impact of all parameters and the fractional order on the model and observed that the system exhibited various behaviors, including tonic firing, periodic firing, and chaotic firing. We also found that the more I tend towards the correct order, the more chaotic modes in the range of parameters. Following this, we coupled the proposed model with a similar one and assessed how the fractional order influences synchronization. Our results demonstrated that the fractional order significantly improves synchronization. The results of this research emphasize that the combination of memristor and discrete neurons provides an effective tool for modeling and estimating biophysical effects in neurons and artificial neural networks.

Dynamical systems that exhibit a high degree of sensitivity to the parameters of their initial states are referred to as chaotic. Natural selection and the process of evolution are the models that inspire a group of optimization algorithms collectively referred to as evolutionary algorithms (EA). EA is quite beneficial when handling difficult optimization difficulties, especially in situations where traditional procedures are either not practical or insufficient. The resolution of goal conflicts is accomplished through multi-objective optimization (MOO). The study proposed using chaotic systems and evolutionary algorithms to address the issue of multi-objective optimization.An initially chaotic time series of wind speed predictions was gathered from three locations in Penglai, China. The preprocessing of these data was carried out using Z-score normalization. We suggested using multi-objective particle swarm optimization (MOPSO) to gather information. Before the suggested design can be applied to the MOPSO of the chaotic system itself, it is required to evaluate the architecture of the proposed that will be utilized, the functioning of the chaotic systems, and the problems in the design of the system. Studies using currently available methods demonstrate that the proposed method outperforms all parameter measurements in terms of 15bits of throughput, active power loss 6.4812 MVA, 0.6495 voltages, 6.8% of RMSE, 0.8% of MAPE, and 0.1 sec of time. The finding of combining evolutionary algorithms with chaotic systems yields a powerful and effective framework for addressing multi-objective optimization problems, which bodes well for practical implementations in fields like building design, economics, and time management. [ABSTRACT FROM AUTHOR]

In this paper, we use two Fractional-Order Chaotic Systems (FOCS)—one for the sender and one for the receiver—to determine the optimal synchronisation for a secure communication technique. With the help of the Step-By-Step Sliding-Mode Observer (SBS-SMO), this synchronisation is accomplished. An innovative optimisation method, known as the artificial Harris hawks optimisation (HHO), was employed to enhance the observer's performance. This method eliminates the random parameter selection process and instead selects the optimal values for the observer. In a short amount of time, the secret message that could have been in the receiver portion (signal, voice, etc.) was successfully recovered using the proposed scheme. The experimental validation of the numerical results was carried out with the assistance of an Arduino microcontroller and several electronic components. In addition, the findings of the experiments were compared with the theoretical calculations, revealing a satisfactory level of agreement. [ABSTRACT FROM AUTHOR]

In this study, for the first time in the literature, identification of different chaotic systems by classifying graphic images of their time series with deep learning methods is aimed. For this purpose, a data set is generated that consists of the graphic images of time series of the most known three chaotic systems: Lorenz, Chen, and Rossler systems. The time series are obtained for different parameter values, initial conditions, step size and time lengths. After generating the data set, a high-accuracy classification is performed by using transfer learning method. In the study, the most accepted deep learning models of the transfer learning methods are employed. These models are SqueezeNet, VGG-19, AlexNet, ResNet50, ResNet101, DenseNet201, ShuffleNet and GoogLeNet. As a result of the study, classification accuracy is found between 96% and 97% depending on the problem. Thus, this study makes association of real time random signals with a mathematical system possible. [ABSTRACT FROM AUTHOR]

The variable-order fractional (VOF) chaotic systems offer a promising solution for applications in secure communication due to their unique properties. This paper addresses the synchronisation problem in secure communication for these systems, which have uncertainties and external disturbances with unknown bounds. According to the variable-order fractional type Mittag-Leffler stability theorem, a fractional-order derivative is applied to a sliding surface, and suitable adaptive laws are devised to address uncertainties and disturbances. A variable-order fractional control strategy and a new criterion are developed to ensure the synchronisation error systems achieve asymptotic stability in finite time, for which the upper limit can be obtained. Simulation outcomes demonstrate the efficacy of the proposed synchronisation strategy in secure communication scenarios. [ABSTRACT FROM AUTHOR]

In this study, encrypted image transmission was carried out with a secure communication application using reversible chaotic image encryption with the synchronization of two identical chaotic systems. Encryption and decryption of the image can be done with the same algorithm using the same chaotic signal. The image can be encrypted using the same chaotic signal on the sending side and decoded with the encryption algorithm and chaotic signal on the receiving side. Experimental results show that the proposed encryption algorithm can securely encrypt and transfer images in 24-bit RGB and 8-bit grayscale images. In the study, histogram, histogram variance, salt & pepper, speckle, NPCR and UACI, four classical types of attacks, NIST, key sensitive and crop visual and statistical attacks were made on encrypted images and the robustness of the encryption method was tested. In addition, PSNR, SSIM, UIQ, BER and NCC image quality criteria were used and the results of attacks on chaotic encrypted images were measured. As a result of visual and statistical attacks, it has been seen that the proposed chaotic encryption algorithm is resistant to attacks. The NPCR and UACI analysis results of the proposed method were compared with the results of similar studies in the literature. According to similar chaotic image coding studies in the literature, the NPCR and UACI values of the proposed method gave better results than most. As a result of the tests, with the secure communication application of the proposed method, image encryption and decryption can be performed by using a common chaotic signal on the sender and receiver sides. [ABSTRACT FROM AUTHOR]

Predicting and understanding the behavior of dynamic systems have driven advancements in various approaches, including physics-based models and data-driven techniques like deep neural networks. Chaotic systems, with their stochastic nature and unpredictable behavior, pose challenges for accurate modeling and forecasting, especially during extreme events. In this paper, we propose a novel deep learning framework called Attractor-Inspired Deep Learning (AiDL), which seamlessly integrates actual statistics and mathematical models of system kinetics. AiDL combines the strengths of physics-informed machine learning and data-driven methods, offering a promising solution for modeling nonlinear systems. By leveraging the intricate dynamics of attractors, AiDL bridges the gap between physics-based models and deep neural networks. We demonstrate the effectiveness of AiDL using real-world data from various domains, including catastrophic weather mechanics, El Niño cycles, and disease transmission. Our empirical results showcase AiDL's ability to substantially enhance the modeling of extreme events. The proposed AiDL paradigm holds promise for advancing research in Time Series Prediction of Extreme Events and has applications in real-world chaotic system transformations. [ABSTRACT FROM AUTHOR]

In the field of Electronic Health (e-Health), Electronic Health Records (EHR) are transmitted between health professionals using e-Health systems for cooperative medical practice, medical monitoring, telemedical expertise, and telemedical imaging. Medical images are a crucial component of EHR and are used in various aspects of telemedicine systems such as expertise, consultation, teaching, and research. However, protecting the authenticity and copyrights of medical images is essential to prevent duplication, modification, or unauthorized distribution. This paper proposes a robust medical image copyright protection method that uses patient palm-print template as watermark and Lorenz chaotic map for template concealing and selecting the appropriate embedding positions in medical images. The novelty of the method lies in optimizing the expected number of modifications per pixel of the medical images after being watermarked. Experimental results indicate that this approach has a high performance with a genuine accept rate of 99.86% and can withstand various image processing attacks, including Gaussian noise, compression, and image rotations, while ensuring personal data security during telemedicine data exchange.

Abstract Predicting and understanding the behavior of dynamic systems have driven advancements in various approaches, including physics-based models and data-driven techniques like deep neural networks. Chaotic systems, with their stochastic nature and unpredictable behavior, pose challenges for accurate modeling and forecasting, especially during extreme events. In this paper, we propose a novel deep learning framework called Attractor-Inspired Deep Learning (AiDL), which seamlessly integrates actual statistics and mathematical models of system kinetics. AiDL combines the strengths of physics-informed machine learning and data-driven methods, offering a promising solution for modeling nonlinear systems. By leveraging the intricate dynamics of attractors, AiDL bridges the gap between physics-based models and deep neural networks. We demonstrate the effectiveness of AiDL using real-world data from various domains, including catastrophic weather mechanics, El Niño cycles, and disease transmission. Our empirical results showcase AiDL’s ability to substantially enhance the modeling of extreme events. The proposed AiDL paradigm holds promise for advancing research in Time Series Prediction of Extreme Events and has applications in real-world chaotic system transformations.