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In insecure communication environments where the communication bandwidth is limited, important image data must be compressed and encrypted for transmission. However, existing image compression and encryption algorithms suffer from poor image reconstruction quality and insufficient image encryption security. To address these problems, this paper proposes an image-compression and encryption scheme based on a newly designed hyperchaotic system and two-dimensional compressed sensing (2DCS) technique. In this paper, the chaotic performance of this hyperchaotic system is verified by bifurcation diagrams, Lyapunov diagrams, approximate entropy, and permutation entropy, which have certain advantages over the traditional 2D chaotic system. The new 2D chaotic system as a pseudo-random number generator can completely pass all the test items of NIST. Meanwhile, this paper improves on the existing 2D projected gradient (2DPG) algorithm, which improves the quality of image compression and reconstruction, and can effectively reduce the transmission pressure of image data confidential communication. In addition, a new image encryption algorithm is designed for the new 2D chaotic system, and the security of the algorithm is verified by experiments such as key space size analysis and encrypted image information entropy.

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This paper, offers a new method for simulating variable-order fractional differential operators with numerous types of fractional derivatives, such as the Caputo derivative, the Caputo-Fabrizio derivative, the Atangana-Baleanu fractal and fractional derivative, and the Atangana-Baleanu Caputo derivative via power-law kernels. Modeling chaotical systems and nonlinear fractional differential equations can be accomplished with the utilization of variable-order differential operators. The computational structures are based on the fractional calculus and Newton's polynomial interpolation. These methods are applied to different variable-order fractional derivatives for Wang-Sun, Rucklidge, and Rikitake systems. We illustrate this novel approach's significance and effectiveness through numerical examples.

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In this paper, in order to realize the predefined-time control of n-dimensional chaotic systems with disturbance and uncertainty, a disturbance observer and sliding mode control method were presented. A sliding manifold was designed for ensuring that when the error system runs on it, the tracking error was stable within a predefined time. A sliding mode controller was developed which enabled the dynamical system to reach the sliding surface within a predefined time. The total expected convergence time can be acquired through presetting two predefined-time parameters. The results demonstrated the feasibility of the proposed control method.

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While encrypting information with color images, most encryption schemes treat color images as three different grayscale planes and encrypt each plane individually. These algorithms produce more duplicated operations and are less efficient because they do not properly account for the link between the various planes of color images. In addressing the issue, we propose a scheme that thoroughly takes into account the relationship between pixels across different planes in color images. First, we introduce a new 1D chaotic system. The performance analysis shows the system has good chaotic randomness. Next, we employ a shortest-path cross-plane scrambling algorithm that utilizes an enhanced Dijkstra algorithm. This algorithm effectively shuffles pixels randomly within each channel of a color image. To accomplish cross-plane diffusion, our approach is then integrated into the adaptive diffusion algorithm. The security analysis and simulation results demonstrate that the approach can tackle the issue of picture loss in telemedicine by encrypting color images without any loss of quality. Furthermore, the images we utilize are suitable for both standard RGB and medical images. They incorporate more secure and highly sensitive keys, robustly withstanding various typical ciphertext analysis attacks. This ensures a reliable solution for encrypting original images.

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In this paper, neural network control of fractional order chaotic systems (FOCSs) with input saturation and unknown sign of the controller gain is addressed by employing the Nussbaum function, where neural networks are utilized to model system uncertainties. To get rid of the limitation that reaching phase should be active before sliding motion in the traditional sliding mode control, a stable sliding surface is constructed. Then, by using the integer order Nussbaum gain control method, a novel controller with neural network sliding mode variable structure is designed. Finally, the practicality of the designed method is confirmed by a simulation experiment.

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In this article, examine the performance of a physics informed neural networks (PINN) intelligent approach for predicting the solution of non-linear Lorenz differential equations. The main focus resides in the realm of leveraging unsupervised machine learning for the prediction of the Lorenz differential equation associated particle swarm optimization (PSO) hybridization with the neural networks algorithm (NNA) as ANN-PSO-NNA. In particular embark on a comprehensive comparative analysis employing the Lorenz differential equation for proposed approach as test case. The nonlinear Lorenz differential equations stand as a quintessential chaotic system, widely utilized in scientific investigations and behavior of dynamics system. The validation of physics informed neural network (PINN) methodology expands to via multiple independent runs, allowing evaluating the performance of the proposed ANN-PSO-NNA algorithms. Additionally, explore into a comprehensive statistical analysis inclusive metrics including minimum (min), maximum (max), average, standard deviation (S.D) values, and mean squared error (MSE). This evaluation provides found observation into the adeptness of proposed AN-PSO-NNA hybridization approach across multiple runs, ultimately improving the understanding of its utility and efficiency.

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Research on switchable chaotic systems with a large range of parameters is scarce. To explore the chaotic characteristics of such systems, this paper proposes new switchable methods by modifying the nonlinear term in the system, resulting in a chaotic system with different nonlinear terms. The unknown parameters in the nonlinear term exhibit different numerical relationships under various combined conditions, and some parameters may tend towards positive infinity. The chaos characteristics are verified by applying a specific switching method to the unified chaotic system. The pseudo-randomness of the random sequence generated by the dissipative system is verified using the NIST test. Finally, the circuit simulation of the system under various switching conditions is performed by selecting different circuit components and adjusting the resistance values.The switching chaotic system is implemented physically on FPGA and breadboard, and the effectiveness of the system is verified.

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We introduce the Discrete-Temporal Sobolev Network (DTSN), a neural network loss function that assists dynamical system forecasting by minimizing variational differences between the network output and the training data via a temporal Sobolev norm. This approach is entirely data-driven, architecture agnostic, and does not require derivative information from the estimated system. The DTSN is particularly well suited to chaotic dynamical systems as it minimizes noise in the network output which is crucial for such sensitive systems. For our test cases we consider discrete approximations of the Lorenz-63 system and the Chua circuit. For the network architectures we use the Long Short-Term Memory (LSTM) and the Transformer. The performance of the DTSN is compared with the standard MSE loss for both architectures, as well as with the Physics Informed Neural Network (PINN) loss for the LSTM. The DTSN loss is shown to substantially improve accuracy for both architectures, while requiring less information than the PINN and without noticeably increasing computational time, thereby demonstrating its potential to improve neural network forecasting of dynamical systems.

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This paper introduces a novel three-dimensional chaotic system that exhibits diverse dynamic behaviors as parameters vary, including phase trajectory offset behaviors and expansion-contraction phenomena. This model encompasses a broad chaotic range and proves suitable for integration within image encryption. Building upon this chaotic system, the study devised a fast image encryption algorithm with an adaptive mechanism, capable of autonomously determining optimal encryption strategies to enhance algorithm security. In pursuit of heightened encryption speed, an FPGA-based chaotic sequence generator was developed for the image encryption algorithm, leveraging the proposed chaotic system. Furthermore, a more efficient scrambling algorithm was devised. Experimental results underscore the superior performance of this algorithm in terms of both encryption duration and security.

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Images, as a crucial information carrier in the era of big data, are constantly generated, stored, and transmitted. Determining how to guarantee the security of images is a hot topic in the information security community. Image encryption is a simple and direct approach for this purpose. In order to cope with this issue, we propose a novel scheme based on eight-base DNA-level permutation and diffusion, termed as EDPD, for color image encryption in this paper. The proposed EDPD integrates secure hash algorithm-512 (SHA-512), a four-dimensional hyperchaotic system, and eight-base DNA-level permutation and diffusion that conducts on one-dimensional sequences and three-dimensional cubes. To be more specific, the EDPD has four main stages. First, four initial values for the proposed chaotic system are generated from plaintext color images using SHA-512, and a four-dimensional hyperchaotic system is constructed using the initial values and control parameters. Second, a hyperchaotic sequence is generated from the four-dimensional hyperchaotic system for consequent encryption operations. Third, multiple permutation and diffusion operations are conducted on different dimensions with dynamic eight-base DNA-level encoding and algebraic operation rules determined via the hyperchaotic sequence. Finally, DNA decoding is performed in order to obtain the cipher images. Experimental results from some common testing images verify that the EDPD has excellent performance in color image encryption and can resist various attacks.

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Over the past few years, chaotic image encryption has gained extensive attention. Nevertheless, the current studies on chaotic image encryption still possess certain constraints. To break these constraints, we initially created a two-dimensional enhanced logistic modular map (2D-ELMM) and subsequently devised a chaotic image encryption scheme based on vector-level operations and 2D-ELMM (CIES-DVEM). In contrast to some recent schemes, CIES-DVEM features remarkable advantages in several aspects. Firstly, 2D-ELMM is not only simpler in structure, but its chaotic performance is also significantly better than that of some newly reported chaotic maps. Secondly, the key stream generation process of CIES-DVEM is more practical, and there is no need to replace the secret key or recreate the chaotic sequence when handling different images. Thirdly, the encryption process of CIES-DVEM is dynamic and closely related to plaintext images, enabling it to withstand various attacks more effectively. Finally, CIES-DVEM incorporates lots of vector-level operations, resulting in a highly efficient encryption process. Numerous experiments and analyses indicate that CIES-DVEM not only boasts highly significant advantages in terms of encryption efficiency, but it also surpasses many recent encryption schemes in practicality and security.

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In this paper, a framework for authorization and personal image protection that applies user accounts, passwords, and personal I-vectors as the keys for ciphering the image content was developed and connected. There were two main systems in this framework. The first involved a speaker verification system, wherein the user entered their account information and password to log into the system and provided a short voice sample for identification, and then the algorithm transferred the user's voice (biometric) features, along with their account and password details, to a second image encryption system. For the image encryption process, the account name and password presented by the user were applied to produce the initial conditions for hyper-chaotic systems to generate private keys for image-shuffling and ciphering. In the final stage, the biometric features were also applied to protect the content of the image, so the encryption technology would be more robust. The final results of the encryption system were acceptable, as a lower correlation was obtained in the cipher images. The voice database we applied was the Pitch Tracking Database from the Graz University of Technology (PTDB-TUG), which provided the microphone and laryngoscope signals of 20 native English speakers. For image processing, four standard testing images from the University of Southern California-Signal and Image Processing Institute (USC-SIPI), including Lena, F-16, Mandrill, and Peppers, were presented to further demonstrate the effectiveness and efficiency of the smart image encryption algorithm.

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Introduction: With the rapid advancement of artificial intelligence (AI) technology, the protection of patient medical image privacy and security has become a critical concern in current research on image privacy protection. However, traditional methods for encrypting medical images have faced criticism due to their limited flexibility and inadequate security. To overcome these limitations, this study proposes a novel chaotic medical image encryption method, called AT-ResNet-CM, which incorporates the attention mechanism fused with the ResNet model. Methods: The proposed method utilizes the ResNet model as the underlying network for constructing the encryption and decryption framework. The ResNet's residual structure and jump connections are employed to effectively extract profound information from medical images and expedite the model's convergence. To enhance security, the output of the ResNet model is encrypted using a logistic chaotic system, introducing randomness and complexity to the encryption process. Additionally, an attention mechanism is introduced to enhance the model's response to the region of interest within the medical image, thereby strengthening the security of the encrypted network. Results: Experimental simulations and analyses were conducted to evaluate the performance of the proposed approach. The results demonstrate that the proposed method outperforms alternative models in terms of encryption effectiveness, as indicated by a horizontal correlation coefficient of 0.0021 and information entropy of 0.9887. Furthermore, the incorporation of the attention mechanism significantly improves the encryption performance, reducing the horizontal correlation coefficient to 0.0010 and increasing the information entropy to 0.9965. These findings validate the efficacy of the proposed method for medical image encryption tasks, as it offers enhanced security and flexibility compared to existing approaches. Discussion: In conclusion, the AT-ResNet-CM method presents a promising solution to address the limitations of traditional encryption techniques in protecting patient medical images. By leveraging the attention mechanism fused with the ResNet model, the method achieves improved security and flexibility. The experimental results substantiate the superiority of the proposed method in terms of encryption effectiveness, horizontal correlation coefficient, and information entropy. The proposed method not only addresses the shortcomings of traditional methods but also provides a more robust and reliable approach for safeguarding patient medical image privacy and security.

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This work deals with a systematic approach for the investigation of compound difference anti-synchronization (CDAS) scheme among chaotic generalized Lotka-Volterra biological systems (GLVBSs). First, an active control strategy (ACS) of nonlinear type is described which is specifically based on Lyapunov's stability analysis (LSA) and master-slave framework. In addition, the biological control law having nonlinear expression is constructed for attaining asymptotic stability pattern for the error dynamics of the discussed GLVBSs. Also, simulation results through MATLAB environment are executed for illustrating the efficacy and correctness of considered CDAS approach. Remarkably, our attained analytical outcomes have been in outstanding conformity with the numerical outcomes. The investigated CDAS strategy has numerous significant applications to the fields of encryption and secure communication.

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Recent advances in optimal diabetes control have made it possible for diabetic patients to live longer, healthier, and happier lives. In this research, particle swarm optimization and genetic algorithm are applied in order to control the non-linear fractional order chaotic system of glucose-insulin optimally. A fractional system of differential equations discussed the chaotic behavior of the growth of the blood glucose system. Particle swarm optimization and genetic algorithm were used to solve the presented optimal control problem. The results showed that when the controller is applied from the beginning, the results of the genetic algorithm method are excellent. All the results obtained for the particle swarm optimization method show that this method is also very successful and the results are very close to the genetic algorithm method.

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In this work, the problem of master-slave outer synchronization in different inner-outer network topologies is presented. Specifically, the studied inner-outer network topologies are coupled in master-slave configuration, where some particular scenarios concerning inner-outer topologies are addressed in order to disclose a suitable coupling strength to achieve outer synchronization. The novel MACM chaotic system is used as a node in the coupled networks, which presents robustness in its bifurcation parameters. Extensive numerical simulations are presented where the stability of the inner-outer network topologies is analyzed through a master stability function approach.

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Image encryption techniques protect private images from unauthorized access while they are being transmitted. Previously used confusion and diffusion processes are risky and time-consuming. Therefore, finding a solution to this problem has become necessary. In this paper, we propose a new image encryption scheme that combines the Intertwining Logistic Map (ILM) and Orbital Shift Pixels Shuffling Method (OSPSM). The proposed encryption scheme applies a technique for confusion inspired by the rotation of planets around their orbits. We linked the technique of changing the positions of planets around their orbits with the shuffling technique of pixels and combined it with chaotic sequences to disrupt the pixel positions of the plain image. First, randomly selected pixels from the outermost orbit are rotated to shift the pixels in that orbit, causing all pixels in that orbit to change their original position. This process is repeated for each orbit until all pixels have been shifted. This way, all pixels are randomly scrambled on their orbits. Later on, the scrambled pixels are converted into a 1D long vector. The cyclic shuffling is applied using the key generated by the ILM to a 1D long vector and reshaped into a 2D matrix. Then, the scrambled pixels are converted into a 1D long vector to apply cyclic shuffle using the key generated by the ILM. After that, the 1D long vector is converted into a 2D matrix. For the diffusion process, using ILM generates a mask image, which is then XORed with the transformed 2D matrix. Finally, a highly secure and unrecognizable ciphertext image is obtained. Experimental results, simulation analysis, security evaluation, and comparison with existing image encryption schemes show that it has a strong advantage in defending against common attacks, and the operating speed of this encryption scheme also performs excellently in practical image encryption applications.

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This paper describes a design process for a universal development kit based on an analog computer concept that can model the dynamics of an arbitrarily complex dynamical system up to the fourth order. The constructed development kit contains digital blocks and associated analog-to-digital and digital-to-analog converters (ADCs and DAC), such that multiple-segmented piecewise-linear input-output characteristics can be used for the synthesis of the prescribed mathematical model. Polynomial input-output curves can be implemented easily by four-quadrant analog multipliers. The proposed kit was verified through several experimental scenarios, starting with simple sinusoidal oscillators and ending with generators of continuous-time robust chaotic attractors. The description of each individual part of the development kit is accompanied by links to technical documentation, allowing skilled readers in the construction of electronic systems to replicate the proposed functional example. For this purpose, the electrical scheme of the hybrid analog computer and all important source codes are available online.

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Existing chaotic system exhibits unpredictability and nonrepeatability in a deterministic nonlinear architecture, presented as a combination of definiteness and stochasticity. However, traditional two-dimensional chaotic systems cannot provide sufficient information in the dynamic motion and usually feature low sensitivity to initial system input, which makes them computationally prohibitive in accurate time series prediction and weak periodic component detection. Here, a natural exponential and three-dimensional chaotic system with higher sensitivity to initial system input conditions showing astonishing extensibility in time series prediction and image processing is proposed. The chaotic performance evaluated theoretically and experimentally by Poincare mapping, bifurcation diagram, phase space reconstruction, Lyapunov exponent, and correlation dimension provides a new perspective of nonlinear physical modeling and validation. The complexity, robustness, and consistency are studied by recursive and entropy analysis and comparison. The method improves the efficiency of time series prediction, nonlinear dynamics-related problem solving and expands the potential scope of multi-dimensional chaotic systems.

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An image encryption algorithm for the double scrambling of the pixel position and bit was cryptanalyzed. In the original image encryption algorithm, the positions of pixels were shuffled totally with the chaotic sequence. Then, the 0 and 1-bit positions of image pixels were scrambled through the use of another chaotic sequence generated by the input key. The authors claimed that the algorithm was able to resist the chosen-plaintext attack. However, through the analysis of the encryption algorithm, it was found that the equivalent key of the whole encryption algorithm was the scrambling sequence T in the global scrambling stage, the pixel bit level scrambling sequence WT and the diffusion sequence S. The generation of scrambling sequence T is related to the sum of all pixel values of the plaintext image, while the generation of WT and S is not associated with the image to be encrypted. By using a chosen-plaintext attack, these equivalent key streams can be cracked so as to realize the decoding of the original chaotic encryption algorithm. Both theoretical analysis and experimental results verify the feasibility of the chosen-plaintext attack strategy. Finally, an improved algorithm was proposed to overcome the defect, which can resist the chosen-plaintext attack and has the encryption effect of a "one time pad".