Tent Map Research Articles

An algorithm for lane detection based on RIME optimization and optimal threshold

In order to address the challenges of low lane line detection rates caused by complex road conditions,we propose a novel algorithm that integrates frost and ice optimisation with optimal thresholding. A pre-processing model based on Retinex theory is used to reduce noise and preserve grey scale detail. The optimal OTSU threshold is determined for segmentation, which is enhanced by tent mapping. To further enhance the precision of the detection process, the binarized image is transformed into a bird’s-eye view, and the lane line pixel features are identified through the use of an adaptive sliding window. Ultimately, the RANSAC algorithm is utilized in conjunction with a parabolic model for lane line fitting. The experimental results demonstrate that, in comparison to similar image segmentation algorithms, the proposed method exhibits a notable advantage in terms of threshold calculation error and computational efficiency. Moreover, in comparison to analogous line detection algorithms, the detection accuracy rate reaches 93.87%, effectively reducing the impact of interference factors and demonstrating remarkable robustness that surpasses the traditional Hough Transform, which has an accuracy of 43.2%, and sliding window and Hough transform, with an accuracy of 89.16%. The code of our research work is publicly available at: https://github.com/zx2000430/rime.

Deep learning for prediction and classifying the dynamical behaviour of piecewise-smooth maps

This paper explores novel ways of predicting and classifying the dynamics of piecewise smooth maps using various deep learning models. Moreover, we have used machine learning models such as Decision Tree Classifier, Logistic Regression, K-Nearest Neighbor, Random Forest, and Support Vector Machine for predicting the border collision bifurcation in the 1D normal form map and the 1D tent map. The decision tree classifier best predicts the border collision bifurcation for the 1D normal form map, the random forest, and the 1D tent map. This study introduces a novel application of deep learning models to cobweb diagrams and phase portraits, which provides a new perspective for classifying regular and chaotic behaviour. Further, we classified the regular and chaotic behaviour of the 1D tent map and the 2D Lozi map using deep learning models like Convolutional Neural Network (CNN), ResNet50, and ConvLSTM via cobweb diagram and phase portraits, where CNN exhibits better performance than other models. We also classified the chaotic and hyperchaotic behaviour of the 3D piecewise smooth map using deep learning models such as the Feed Forward Neural Network (FNN), Long Short-Term Memory (LSTM), and Recurrent Neural Network (RNN). We have shown that LSTM performs best for classifying chaotic and hyperchaotic behaviour. Additionally, LSTM outperforms other models in accuracy and computational efficiency, making it highly effective for real-time analysis. Finally, deep learning models such as Long Short Term Memory (LSTM) and Recurrent Neural Network (RNN) are used for reconstructing the two-parameter bifurcation charts of 2D normal form map, in which LSTM is more precise than RNN in reconstructing the two-parametric charts.

A robust approach to satellite image encryption using chaotic map and circulant matrices

AbstractIn the modern era, where satellite imagery is vital for applications like ecological monitoring and national security, ensuring the safety and integrity of these data repositories is crucial. This study presents an improved satellite image encryption technique that combines the cryptographic strength of the circulant matrix in the Hill cipher with the dynamic characteristics of the hyperbolic tangent tent map, further enhanced by the Kronecker XOR product. The algorithm initiates with computing alterations by a shift amount. After preserving the leftmost pixel in each row, it executes XOR operations between alternating rows, combining the value of the current even or odd row with corresponding pixels in the adjacent rows followed by encryption using the Hill cipher. The resulting image undergoes a diffusion process utilizing a hyperbolic tangent tent map. The Kronecker XOR product operation is then applied to individual pixels to produce a secure image followed by additional diffusion with keys from the hyperbolic tangent tent map to achieve the final encrypted image. We conducted simulations using MATLAB to assess the efficiency of the proposed satellite image encryption from theoretical and statistical perspectives. The results exhibit robust encryption performance as demonstrated by metrics such as an entropy value of 7.9982, a UACI of 33.5333%, and an NPCR of 99.6038%. The experiment results demonstrate the proposed image encryption scheme's reliability, practicability, and efficiency in securing satellite images during data storage and transmission. Comprehensive testing against various attacks including correlation, histogram, chi‐square, NPCR, PSNR, UACI, SSIM, key space and key sensitivity analysis confirms the scheme's robustness, efficiency and speed. These findings verify the scheme's ability to come across the most stringent encryption and decryption standards, making it an effective solution for securing sensitive satellite image data.

Enhanced lightweight encryption algorithm based on chaotic systems

In order to improve security and efficiency, this study presents a novel lightweight encryption technique that makes use of chaotic systems. Our method creatively combines the new chaotic KLEIN_64 algorithm with the Keccak-256 hash function, offering a solid basis for producing initial values essential for causing chaotic maps during the encryption process. After a deep validation with rigorous NIST testing, our chaotic pseudo random generator, LAC, exhibits excellent reliability and cryptographic robustness. Furthermore, the complexity of the cryptographic round function is improved by incorporating a second chaotic pseudo random generator that combines chaotic LFSR and Skew Tent Maps, thereby fortifying security measures.Designed with resource-limited applications in mind, our approach ensures that the cryptosystem remains both lightweight and efficient, meeting the stringent constraints typical of such environments. The practical feasibility and performance of our approach are extensively evaluated through FPGA implementation on the Zybo 7Z010 platform. Our implementation achieves a remarkable throughput of 2.820 Gbps while maintaining optimal resource utilization and efficiency. Extensive experimental results confirm the superior security of our cryptosystem, with correlation tests, entropy measurement, and histogram analysis showcasing robustness against statistical attacks. Moreover, the cryptosystem shows little fluctuation in the Unified Average Changing Intensity (UACI) and Non-Linear Pixel Change Rate (NPCR), confirming its resistance to differential attacks. Overall, our technique advances lightweight cryptography by providing a robust and efficient solution to modern cybersecurity challenges. In particular, our approach is well-suited for applications with limited resources, ensuring that security is maintained without compromising on performance or efficiency, thus fulfilling the needs of modern, constrained environments.

Periodic Nature in General System and Cellular Automata

Introduction: In this research paper we have discussed the various periodic points in general systems and established relation among them by adopting strong conditions to them so we can relate smoothly. Additionally, we developed the relationship with the dynamical systems and derived periodic points in Tent maps and circular maps in general systems. We established the fundamental characteristics of cellular automata in general systems, such as continuity. Furthermore, we covered periodic points in additive CAs with radius zero and the inverse of a periodic point in additive cellular automata. Objectives: To be familiar with the relationships between different periodic points in a general system, general system examples, and the contrast between the periodic behavior of a dynamical system and a new system. Explaining periodic nature in additive form and defining cellular automata in a new framework. Methods: We employed fundamental notions of dynamical systems and the definition of cellular automata in a new system. Results and Conclusion: The relationships between different periodic points in a general system, periodic points in a new system, the periodic nature of additive cellular automata in the new system, and its basic characteristics were all revealed to us.

An Innovative Algorithm Based on Chaotic Maps Amalgamated with Bit-Level Permutations for Robust S-Box Construction and Its Application in Medical Image Privacy

Data security and privacy have become essential due to the increasingly advanced interconnectivity in today’s world, hence the reliance on cryptography. This paper introduces a new algorithm that uses a novel hybrid Tent–May chaotic map to generate pseudo-random numbers, as well as block encryption. We design a robust S-box by combining the Tent and May Maps, which yields a chaotic system with improved cryptographic properties. This S-box is a critical cryptographic primitive that significantly improves encryption security and leverages the strengths of both maps. The encryption process involves two key steps: block-wise substitution and permutation. First, we divide the image into 16×16 blocks, then substitute each pixel with the 8−byte key and S-box. Next, we convert the encrypted image back into vector form, reorganize it using the permutation vector based on the subgroups of S16, and finally return it to its original form. This approach greatly improves block cipher security when used, especially to protect medical images by guaranteeing their confidentiality and noninterference. Performance measures like PSNR, UACI, MSE, NCC, AD, SC, MD, and NAE prove how immune our method is to various cryptographic and statistical attacks, making it more accurate and more secure than the existing techniques.

Chaos based image encryption scheme to secure sensitive multimedia content in cloud storage

Cloud computing offers a variety of on-demand services to users and has gained significant prominence in the contemporary era. The security of information stored in cloud data centers has become a central concern, especially for sensitive data like medical images, videos, and multimedia content that require heightened protection when stored in data centers. Cloud users have a responsibility to ensure the security of their data through strategic measures. Focusing on maintaining the privacy of images stored in the cloud, this research introduces an innovative image encryption technique that is based on a modified Skew Tent chaotic map. The suggested modification to the chaotic map includes combining the Skew Tent map with both the sine trigonometric function and perturbation technology. This results in enhanced randomness, more intricate dynamical behavior, a broader chaotic range, and increased sensitivity to initial values in contrast to alternative chaotic maps. The incorporation of this adapted map into a stepwise procedure, involving two rounds of permutation followed by diffusion, effectively accomplishes image data encryption for cloud storage systems. These consecutive operations collectively enhance the encryption method’s randomness and robustness. Through simulations conducted using Cloudsim, the cipher-image exhibits a uniform distribution and achieves a commendable information entropy score of 7.996749. The encryption algorithm significantly reduces correlation coefficients from 1 in the original image to 0 in the encrypted image, while maintaining NPCR (Number of Pixel Change Rate) and UACI (Unified Average Changing Intensity) values within the critical range. Additionally, both theoretical analysis and practical evaluations confirm the algorithm’s resilience against exhaustive, occlusion, and classical attacks. Moreover, extending this encryption framework to video data, a novel video encryption approach is proposed.

A High-Performance FPGA PRNG Based on Multiple Deep-Dynamic Transformations.

Pseudo-random number generators (PRNGs) are important cornerstones of many fields, such as statistical analysis and cryptography, and the need for PRNGs for information security (in fields such as blockchain, big data, and artificial intelligence) is becoming increasingly prominent, resulting in a steadily growing demand for high-speed, high-quality random number generators. To meet this demand, the multiple deep-dynamic transformation (MDDT) algorithm is innovatively developed. This algorithm is incorporated into the skewed tent map, endowing it with more complex dynamical properties. The improved one-dimensional discrete chaotic mapping method is effectively realized on a field-programmable gate array (FPGA), specifically the Xilinx xc7k325tffg900-2 model. The proposed pseudo-random number generator (PRNG) successfully passes all evaluations of the National Institute of Standards and Technology (NIST) SP800-22, diehard, and TestU01 test suites. Additional experimental results show that the PRNG, possessing high novelty performance, operates efficiently at a clock frequency of 150 MHz, achieving a maximum throughput of 14.4 Gbps. This performance not only surpasses that of most related studies but also makes it exceptionally suitable for embedded applications.

Energy consumption prediction of coal-fired unit boiler system based on different operating states

ABSTRACT The energy consumption of the coal-fired unit’s boiler system varies significantly when accommodating flexible peak shaving demands. To aid staff in comprehending the boiler’s operational status and optimize its performance, a prediction model of the energy consumption of the boiler system was established based on the different states of the unit operation. First, a dataset of boiler energy consumption under variable load was established based on theory of fuel-specific consumption, and the Mean Impact Value (MIV) algorithm was used to simplify the input features of the model. Second, the Aquila Optimizer (AO) with tent map, adaptive t-distribution, and opposites learning mechanism was introduced to determine the parameters in the prediction model. On this basis, the sliding-window method was used to classify the operating states based on the load of the unit, and the original dataset without operating state distinction, the steady state operating data, the load uplink data, and the load downlink data were used to establish Models 1–4, respectively. The result shows that Model 1 outperforms Model 2 with 24.45% and 18.22% lower aMAE and aRMSE, respectively. compared to Model 3, it shows a decrease of 24.07% and 16.98%. Compared to Model 1, Model 4 shows a reduction of 20.52% and 18.91% in aMAE and aRMSE, respectively. This indicates that distinguishing different operating states to establish boiler energy consumption prediction models can obtain better prediction accuracy.

Modulated Radio Frequency Stealth Waveforms for Ultra-Wideband Radio Fuzes.

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.

Synchronization transition in space–time chaos in the presence of quenched disorder

Synchronization of two replicas of coupled map lattices for continuous maps is known to be in the multiplicative noise universality class. We study this transition in the presence of quenched disorder in coupling. The disorder is identical in both replicas. We study one-dimensional, two-dimensional, and globally coupled logistic and tent maps. We observe a clear second-order transition with new exponents. The order parameter decays as t−δ and δ depends on the map and its parameters. The asymptotic order parameter for Δ distance from a critical point grows as Δβ with β∼δ. The quenched disorder in coupling is a relevant perturbation for the replica synchronization of coupled map lattices. The critical exponents are different from those of the multiplicative noise universality class. However, it does not depend on dimensionality in the cases studied if the transition is continuous.

Research on short-term photovoltaic power generation forecasting model based on multi-strategy improved squirrel search algorithm and support vector machine

Solar photovoltaic (PV) power generation is susceptible to environmental factors, and redundant features can disrupt prediction accuracy. To achieve rapid and accurate online prediction, we propose a method that combines Principal Component Analysis (PCA) with a multi-strategy improved Squirrel Search Algorithm (SSA) to optimize Support Vector Machine (MISSA-SVM) for prediction. Initially, to mitigate the impact of redundant features on prediction accuracy, KPCA is employed for feature dimensionality reduction. Subsequently, SVM is suggested as the foundational algorithm for constructing the prediction model. Furthermore, to address the influence of hyperparameter selection on model performance, SSA is introduced for optimizing SVM hyperparameters, with the aim of establishing the optimal prediction model. Moreover, to enhance solution efficiency and accuracy, a multi-strategy approach termed MISSA is proposed, which integrates Population Initialization based on the Tent map, Nonlinear Predator Presence Probability, Chaotic-based Dynamic Opposition-based Learning, and Selection Strategy, to refine SSA. Finally, through case studies, the performance of MISSA optimization is assessed using challenging CEC2021 test functions, demonstrating its high optimization performance, stability, and significance. Subsequently, the performance of the prediction model is validated using two datasets, showcasing that the proposed prediction method achieves high accuracy and robust prediction stability.

Robust zero-watermarking algorithm for multi-medical images based on FFST-Schur and Tent mapping

Aiming at issues such as the difficulty of centralized protection of multiple medical images and the high storage cost caused by repetitive operations, we proposed a robust zero-watermarking algorithm for multiple medical images based on fast finite Shearlet transform (FFST)-Schur and Tent mapping. First, multiple medical images were normalized, and the processed images were fused using a gray-weighted average fusion method for image fusion. Second, an FFST is applied to the fused image to divide the low-frequency sub-bands into blocks of the same size and perform Schur decomposition, which generates a feature image using the magnitude between the largest eigenvalue of each block and the overall average value. Finally, an image encryption algorithm based on Tent mapping is proposed to encrypt the logo image, and the encrypted image and feature image are then subjected to an exclusive OR operation to produce a zero-watermarking image. Experimental results demonstrate that the proposed approach effectively safeguards against standard image processing and geometric and combinatorial attacks. The average performance of the anti-attack algorithm was improved by approximately 3.2 % compared to similar algorithms, indicating the superior robustness of the proposed algorithm.

Fractal Tent Map with Application to Surrogate Testing

Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical properties, such as mixing and diffusion. However, chaotic PRNGs have several known shortcomings, e.g., being prone to chaos degeneration, falling in short periods, and having a relatively narrow parameter range. Therefore, it is reasonable to design novel simple chaotic maps to overcome these drawbacks. In this study, we propose a novel fractal chaotic tent map, which is a generalization of the well-known tent map with a fractal function introduced into the right-hand side. We construct and investigate a PRNG based on the proposed map, showing its high level of randomness by applying the NIST statistical test suite. The application of the proposed PRNG to the task of generating surrogate data and a surrogate testing procedure is shown. The experimental results demonstrate that our approach possesses superior accuracy in surrogate testing across three distinct signal types—linear, chaotic, and biological signals—compared to the MATLAB built-in randn() function and PRNGs based on the logistic map and the conventional tent map. Along with surrogate testing, the proposed fractal tent map can be efficiently used in chaos-based communications and data encryption tasks.

Confusion and Diffusion Techniques for Image Encryption Process Based on Chaos System

Face recognition uses biometric technologies to identify humans based on their facial characteristics. This method is commonly used to restrict information access control. The benefits of face recognition systems encompass their ease of use and security. The human face recognition process consists of face detection, face tracking, and face recognition. The process uses some algorithms: the Viola-Jones for face detection, the Kanade-Lucas-Tomasi (KLT) for face tracking, and the principal component analysis (PCA) for face recognition. Furthermore, this research proposed face recognition with an encryption process to protect the data stored in a database. The encryption process consists of two main processes: confusion and diffusion. The confusion process is randomizing the position of the original image pixels. This research utilized the Arnold’s cat map (ACM) for the confusion process, and the diffusion process was performed using the XOR operation with the key generated from the 1D chaos system. Three different 1D chaos systems, namely logistic map, Bernoulli map, and tent map, were compared to see which chaos system had the best encryption results. Tests were conducted by comparing various parameters on the three proposed 1D chaos systems, including correlation coefficient, histogram analysis, entropy value, number of pixel rate changes (NPCR), and unified average change intensity (UACI). Based on testing the image encryption results, the diffusion process utilizing the tent map produced the best image encryption compared to other chaotic systems.

Investigation of Chaotic Features of the Family of Generalized Tent Maps

Investigation of Chaotic Features of the Family of Generalized Tent Maps

Exploring Simplicity Bias in 1D Dynamical Systems.

Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability-complexity relationships may be a useful tool when studying patterns in dynamical systems.

Periodic Behaviour of General Systems

A continuous function on the product of compact metric spaces to itself and back to the same space is known as a genera system. Where each element's orbit is an infinite sequence and where the first two elements are the same as given and next to it depends on the two elements prior to it form stronger conditions for the orbit. We could define an m-step dynamical system by extending the definition of a compact metric space to its m-times product. Because the system's current state frequently depends directly on the conditions of previous terms, this system appears more realistic. The basic theorems regarding periodic points and their related points, such as fixed point, limit points, recurrent points, will be proved in this paper. We also define the topological transitivity and its properties. In the end we find periodic points with periods one and two for affine maps and periodicity of tent map in dynamical system and generalised dynamical system.

Novel, Fast, Strong, and Parallel: A Colored Image Cipher Based on SBTM CPRNG

Novel, Fast, Strong, and Parallel: A Colored Image Cipher Based on SBTM CPRNG

Cryptanalysis of an image encryption algorithm based on cellular automata and chaotic skew tent map

Cryptanalysis of an image encryption algorithm based on cellular automata and chaotic skew tent map