Logistic Map Research Articles

Binocular camera calibration using a BP algorithm optimized by an improved subtraction-average-based optimizer

The BP algorithm exhibits drawbacks such as reduced precision and extended iteration duration during the process of calibrating a binocular camera system. A technique employing an improved subtraction-average-based optimizer to optimize the BP algorithm (ISABO-BP) is introduced to address these limitations and complete the calibration of the binocular camera. The pixel values of the corner in 2D space and the coordinate values in 3D space are used as the input and output for the BP algorithm, respectively. First, the logistic chaotic mapping is used to initialize the population to increase the diversity of the initial population. The piecewise mapping is employed to generate random values to replace the coefficient values in the individual position update formula, making the population distribution more uniform. The golden sine strategy is adopted to help particles escape from local optima. The ISABO-BP algorithm is utilized to perform the process of calibrating a binocular camera. Then, through numerical experiments, the mean calibration precision for the BP algorithm is 0.1501 and 0.0445 cm for the ISABO-BP algorithm. The calibration precision has been enhanced by 70.4%. The iterative steps of the BP algorithm are 353 epochs, while the ISABO-BP algorithm are 76 epochs, and the iterative speed is increased by nearly four times. It is evident that the ISABO-BP algorithm enhances the calibration precision and expedites the convergence rate. Finally, other intelligent algorithms to optimize the BP algorithm for calibrating a binocular camera are compared, and the superiority of this algorithm is also verified.

Security enhancement for NOMA-PON with 2D cellular automata and Turing pattern cascading scramble aided fixed-point extended logistic chaotic encryption

The non-orthogonal multiple access-passive optical network (NOMA-PON) is facing the dual security threats of primary user interference and unauthorized third-party user eavesdropping, so efficient data security enhancement techniques are crucial. To solve these problems, we propose a fixed-point extended (FE)-logistic chaotic mapping to reduce the computational complexity while employing a two-dimensional (2D) cellular automata (CA) and Turing pattern (TP) cascading scramble (CA-TPCS) encryption algorithm to further improve the sensitivity of the NOMA-PON system. The CA-TPCS consists of 2D-CA dynamic bit encryption and Turing symbol substitution (TSS). By using FE chaos to construct 2D-CA and adopting index sort to extract the TSS matrix, dynamic diffusion of bits and scrambling of a 2D symbol matrix are achieved. To ensure the key privacy, we employ a dual key mechanism, and uplink data is introduced as the private key. To verify the feasibility of the proposed method, a simulation validation is built on a 17.6 Gb/s power division multiplexing-orthogonal frequency division multiplexing (PDM-OFDM) NOMA-PON system transmitted over 25 km standard single mode fiber (SSMF). The results show that the proposed scheme has no effect on the optimal power allocation rate (PAR) values and the values are all 3. Meanwhile, the receiver sensitivity gains of 0.2 and 0.3 dB are obtained for high-power and low-power users after encryption. The ciphertext has good diffusion and statistical properties, and the key space is flexibly controlled by the FE precision f, the length l of the transmitted bit, and the size T of the TP, with the value of 22f+l+T×T. The results show that the proposed scheme is not only very compatible with PDM technology but also can realize the dual defense of internal aggression and external aggression. It has a good application prospect in the future NOMA-PON.

A NEW CONJUGATE GRADIENT METHOD BASED ON LOGISTIC MAPPING FOR UNCONSTRAINED OPTIMIZATION AND ITS APPLICATION IN REGRESSION ANALYSIS

The study tackles the critical need for efficient optimization techniques in unconstrained optimization problems, where conventional techniques often suffer from slow and inefficient convergence. There is still a need for algorithms that strike a balance between computational efficiency and robustness, despite advancements in gradient-based techniques. This work introduces a novel conjugate gradient algorithm based on the logistic mapping formula. As part of the methodology, descent conditions are established, and the suggested algorithm's global convergence properties are thoroughly examined. Comprehensive numerical experiments are used for empirical validation, and the new algorithm is compared to the Polak-Ribière-Polyak (PRP) algorithm. The suggested approach performs better than the PR algorithm, according to the results, and is more efficient since it needs fewer function evaluations and iterations to reach convergence. Furthermore, the usefulness of the suggested approach is demonstrated by its actual use in regression analysis, notably in the modelling of population estimates for the Kurdistan Region of Iraq. In contrast to conventional least squares techniques, the method maintains low relative error rates while producing accurate predictions. All things considered, this study presents the novel conjugate gradient algorithm as an effective tool for handling challenging optimisation problems in both theoretical and real-world contexts.

A Hybrid Approach of Substitution and Permutation techniques for Modern Image-Cryptosystem

Abstract This paper proposes a new image encryption algorithm based on the introduction of cellular automata with Galois field-based methods to further encourage a higher level of security. This begins the encryption process by creating an initial substitution box from the irreducible polynomials in the Galois field, followed by the final substitution box obtained through permutation operations. This lays
the foundation for a sound cryptographic process. In order to handle different cryptographic attack types, balance in the substitution box has been closely analyzed. Additionally, we leverage the chaotic nature of the logistic map to incorporate a random element, significantly strengthening the encryption scheme against diverse cryptanalytic attacks. Nonlinear dynamics, as introduced by cellular automata, further develop the encryption process and disperse the image’s data, making it more intricate for any potential attacker. The differential analysis validates the encryption scheme’s resistance to differential attacks, thereby confirming its potential for secure image transmission and storage. The proposed hybrid approach presents a comprehensive solution for image encryption, ensuring high security and computational efficiency. This contribution is an added advantage in the development of image cryptosystems,
addressing the modern challenges facing secure data within the digital landscape.

A new S-box pattern generation based on chaotic enhanced logistic map: case of 5-bit S-box

AbstractCryptography plays consistently an essential role in securing any sort of communications or data broadcast over the network. Since the security of any designed block cipher algorithm is related to its Substitution box (S-box), several efforts have been made by researchers to design a vigorous S-box that maintains flawlessly the cost, performance, and security trade-off. From the literature, we can find a variety of input–output sizes of S-boxes, each of which has its benefits and drawbacks. Therefore, this work introduces a new S-box pattern generation based on the chaotic enhanced logistic map where its chaotic behavior offers good randomness ability, a fact that enhances its unpredictability. In our realization, the intention was the generation of a 5-bit Sbox due to its suitability and cost-effectiveness to be integrated into lightweight cryptosystems. Moreover, the S-box security strength is proved by testing it through numerous cryptanalysis measurements. We can mention non-linearity, bijectivity, linearity, differential cryptanalysis, boomerang attacks resilience, Avalanche effect, and algebraic attacks resilience. The results show that our proposition provides good resistance to the aforementioned attacks and even shows superiority over its 5-bit competitors in terms of non-linearity, differential, Boomerang, and algebraic attack resistance.

Gumbel–Logistic Unit Distribution with Application in Telecommunications Data Modeling

The manuscript deals with a new unit distribution that depends on two positive parameters. The distribution itself was obtained from the Gumbel distribution, i.e., by its transformation, using generalized logistic mapping, into a unit interval. In this way, the so-called Gumbel-logistic unit (abbr. GLU) distribution is obtained, and its key properties, such as cumulative distribution function, modality, hazard and quantile function, moment-based characteristics, Bayesian inferences and entropy, have been investigated in detail. Among others, it is shown that the GLU distribution, unlike the Gumbel one which is always positively asymmetric, can take both asymmetric forms. An estimation of the parameters of the GLU distribution, based on its quantiles, is also performed, together with asymptotic properties of the estimates thus obtained and their numerical simulation. Finally, the GLU distribution has been applied in modeling the empirical distributions of some real-world data related to telecommunications.

Investigating the dynamics of generalized discrete logistic map

Investigating the dynamics of generalized discrete logistic map

Thumbnail-Preserving Encryption Based on Binary–Decimal Hybrid and a Generalized Coupled Logistic Map

Traditional image encryption methods typically make a trade-off between privacy protection and visual usability. To address this issue, a novel thumbnail-preserving encryption scheme is proposed based on a hybrid of decimal and binary pixel values in three pixel groups, utilizing the excellent dynamic characteristics of a generalized coupled logistic map. Theoretically, it is proved that the core algorithm of this scheme is sum-preserving. Experimentally, it is demonstrated that this scheme not only excels in efficiency and resistance to attacks, effectively safeguarding image privacy, but also retains high-quality thumbnails after encryption, achieving both objectives of image privacy protection and visual usability.

A Study on Future Population Dynamics of Indigenous Earthworm Species in Golaghat District of Assam, India

This study presents a pioneering exploration into the population dynamics of indigenous earthworm species in the Golaghat district of Assam, India, through the lens of mathematical modeling. Recognizing the integral role of earthworms in enhancing soil productivity and ecosystem health, we embarked on a detailed longitudinal analysis spanning from 2018 to 2023 to assess their population trends across different seasons and subdivisions within the district. Utilizing the principles of Mathematical Biology, we employed the Malthus Growth model and the Logistic Growth model to estimate future population trajectories of earthworm species, integrating biological insights with mathematical rigor. Our methodology, combining extensive field data collection with sophisticated mathematical modeling, provides a replicable framework for similar ecological studies. This study contributes to the growing field of Mathematical Biology, offering a novel approach to understanding the complex interactions within ecosystems and the impact of environmental changes on key species. The outcomes offer valuable insights into sustainable agricultural practices and biodiversity conservation in tropical and subtropical regions, emphasizing the critical role of indigenous earthworm species in maintaining soil health and ecosystem services. Our findings reveal significant seasonal variations and highlight the resilience of these species in the face of ecological changes. The models suggest distinct population growth patterns, with the Logistic model providing a more realistic projection considering environmental constraints and resource availability. The bifurcation diagram is drawn for the Logistic map that presents the phenomena inside the chaotic region.

Enhancing the Security and Efficiency of Biomedical Image Encryption through a Novel Hyper-Chaotic Logistic Map

Enhancing the Security and Efficiency of Biomedical Image Encryption through a Novel Hyper-Chaotic Logistic Map

Time Irreversibility of Complex Time Series with Detrended Cross-Correlation Analysis Based on Visibility Graph

In this paper, we introduce detrended cross-correlation analysis (DCCA) method into visibility graph (VG) algorithm and propose VGDCCA method to reflect the time series irreversibility from a new perspective. The validity and reliability of the proposed VGDCCA method is supported by numerical simulations on synthesized short-term correlated chaotic systems and long-term correlated fractal processes, and by the empirical analysis on stock indices and traffic parameter. The VGDCCA planes suggest that autoregressive fractionally integrated moving average (ARFIMA) and fractional Gaussian noise (FGN) series show time reversible behavior, whatever the long-term correlation of the series is or however strong the persistence or anti-persistence of the series is. Meanwhile, Logistic map with [Formula: see text] and Hénon map show more time irreversible behaviors than those of ARFIMA, FGN series and other Logistic maps. It can be found that the relationship between cross-correlation of ingoing degree sequence and outgoing degree sequence for the simulated series with different parameters is consistent with the complexity and autocorrelation behavior in the corresponding definition of the time series. For the empirical analysis, VGDCCA method declares the similarity and dissimilarity between stock indices on time series irreversibility and captures the time irreversibility of traffic time series recorded by the detectors in different locations.

Multi-Search Strategy-based Improved Water Flow Optimizer Algorithm for Cluster Analysis

Clustering is a popular technique that has proven its capability in diverse fields like data analytics, business intelligence, social mining, image recognition, document clustering and bioinformatics. This technique determines the valuable information from a pre-defined set of data and groups similar information into the same cluster. In literature, many algorithms have been presented based on several clustering approaches. It is observed that partitional clustering algorithms are widely popular due to there simplicity and easy implementation such as k-means, k-medoids, and k-harmonic means. However, traditional algorithms suffer from several limitations like being trapped in local optima and depending on the initial solution quality. Heuristic algorithms are also proposed to alleviate the problems of traditional clustering algorithms. But, sometimes, these algorithms also get stuck in local minima and exhibit a lack of balance between search mechanisms. Hence, this work presents an improved water flow optimizer (IWFO) algorithm for cluster analysis that can address the issues of traditional and heuristic algorithms. In the proposed IWFO algorithm, the initial solution is generated based on the logistic chaotic map instead of random initialization, and in turn, an optimal quality solution is generated. The search mechanism of the WFO algorithm is enhanced based on an improved search mechanism which is the combination of non-linear functions and the previous best solution. Further, the local optima issue is alleviated using a multi-start search mechanism. The efficacy of the proposed IWFO algorithm is evaluated using twelve benchmark clustering datasets and results are compared with seventeen clustering algorithms. The simulation results are assessed using intra-cluster distance (intra), standard deviation (SD), rank, accuracy rate (AR) and detection rate (DR) parameters. Further, a statistical test is also conducted to validate the efficacy of the proposed IWFO algorithm. The results showed that proposed IWFO algorithms obtain superior quality results on most of the datasets.

An adaptive robust watermarking scheme based on chaotic mapping

Digital images have become an important way of transmitting information, and the risk of attacks during transmission is increasing. Image watermarking is an important technical means of protecting image information security and plays an important role in the field of information security. In the field of image watermarking technology, achieving a balance between imperceptibility, robustness, and embedding capacity is a key issue. To address this issue, this paper proposes a high-capacity color image adaptive watermarking scheme based on discrete wavelet transform (DWT), Heisenberg decomposition (HD), and singular value decomposition (SVD). In order to enhance the security of the watermark, Logistic chaotic mapping was used to encrypt the watermark image. By adaptively calculating the embedding factor through the entropy of the cover image, and then combining it with Alpha blending technology, the watermark image is embedded into the Y component of the YCbCr color space to enhance the imperceptibility of the algorithm. In addition, the robustness of the algorithm was further improved through singular value correction methods. The experimental results show that the average PSNR and SSIM of the watermarking scheme are 45.3437dB and 0.9987, respectively. When facing various attacks, the average NCC of the extracted watermark reaches above 0.95, indicating good robustness. The embedding capacity of this scheme is 0.6667bpp, which is higher than other watermarking schemes, and the average running time is 1.1136 seconds, which is better than most schemes.

A Multilayer Nonlinear Permutation Framework and Its Demonstration in Lightweight Image Encryption

As information systems become more widespread, data security becomes increasingly important. While traditional encryption methods provide effective protection against unauthorized access, they often struggle with multimedia data like images and videos. This necessitates specialized image encryption approaches. With the rise of mobile and Internet of Things (IoT) devices, lightweight image encryption algorithms are crucial for resource-constrained environments. These algorithms have applications in various domains, including medical imaging and surveillance systems. However, the biggest challenge of lightweight algorithms is balancing strong security with limited hardware resources. This work introduces a novel nonlinear matrix permutation approach applicable to both confusion and diffusion phases in lightweight image encryption. The proposed method utilizes three different chaotic maps in harmony, namely a 2D Zaslavsky map, 1D Chebyshev map, and 1D logistic map, to generate number sequences for permutation and diffusion. Evaluation using various metrics confirms the method’s efficiency and its potential as a robust encryption framework. The proposed scheme was tested with 14 color images in the SIPI dataset. This approach achieves high performance by processing each image in just one iteration. The developed scheme offers a significant advantage over its alternatives, with an average NPCR of 99.6122, UACI of 33.4690, and information entropy of 7.9993 for 14 test images, with an average correlation value as low as 0.0006 and a vast key space of 2800. The evaluation results demonstrated that the proposed approach is a viable and effective alternative for lightweight image encryption.

An enhanced slime mould algorithm with triple strategy for engineering design optimization

Abstract This paper introduces an enhanced slime mould algorithm (EESMA) designed to address critical challenges in engineering design optimization. The EESMA integrates three novel strategies: the Laplace logistic sine map technique, the adaptive t-distribution elite mutation mechanism, and the ranking-based dynamic learning strategy. These enhancements collectively improve the algorithm’s search efficiency, mitigate convergence to local optima, and bolster robustness in complex optimization tasks. The proposed EESMA demonstrates significant advantages over many conventional optimization algorithms and performs on par with, or even surpasses, several advanced algorithms in benchmark tests. Its superior performance is validated through extensive evaluations on diverse test sets, including IEEE CEC2014, IEEE CEC2020, and IEEE CEC2022, and its successful application in six distinct engineering problems. Notably, EESMA excels in solving economic load dispatch problems, highlighting its capability to tackle challenging optimization scenarios. The results affirm that EESMA is a competitive and effective tool for addressing complex optimization issues, showcasing its potential for widespread application in engineering and beyond.

Inversion Analysis for Thermal Parameters of Mass Concrete Based on the Sparrow Search Algorithm Improved by Mixed Strategies

In the traditional mass concrete temperature field calculation, the accuracy of the thermal parameters is extremely important. However, the actual thermal parameters of mass concrete may have some errors with the laboratory-measured values or specification values due to the site ambient temperature, concrete surface insulation measures, cooling water flow, etc. Therefore, it can be combined with the measured temperature of the field temperature sensors using the sparrow search algorithm (SSA) for the inverse analysis of thermal parameters. Firstly, to address the problem that SSA has low convergence accuracy and easily falls into local optimum, a mixed strategy was adopted to improve the algorithm, including Logistic Chaos mapping initialization of the population, the introduction of adaptive weighting factors, and the use of the Cauchy mutation strategy. Then, the performance test was carried out to compare the performance of the algorithm with three different intelligent algorithms and reflect the superiority of the SSA that was improved by mixed strategies (SSAIMSs). Finally, the proposed method was applied to the thermal parameter inversion of a mass concrete pile cap. The inversion results demonstrated that SSAIMSs can improve the accuracy and speed of thermal parameter inversion, and the calculated results of the thermal parameters and temperatures obtained using the SSAIMSs matched well with the measured results in the field, which can meet the accuracy requirements of the actual engineering.

Towards Analysable Chaos-based Cryptosystems: Constructing Difference Distribution Tables for Chaotic Maps

Chaos-based cryptography has yet to achieve practical, real-world applications despite extensive research. A major challenge is the difficulty in analysing the security of these cryptosystems, which often appear ad hoc in design. Unlike conventional cryptography, evaluating the security margins of chaos-based encryption against attacks such as differential cryptanalysis is complex. This paper introduces a straightforward approach of using chaotic maps in cryptographic algorithms in a way that facilitates cryptanalysis. We demonstrate how a chaos-based substitution function can be constructed using fixed-point representation, enabling the application of conventional cryptanalysis tools such as the difference distribution table. As a proof-of-concept, we apply our method to the logistic map, showing that differential properties vary based on the initial state and number of iterations. Our findings demonstrate the feasibility of designing analysable chaos-based cryptographic components with well-understood security margins.

Multiple-image authentication method based on phase-only holograms and a logistic map

An interesting security method for a multiple-image authentication scheme is proposed based on computer-generated holograms and a logistic map. First, each original image is encoded as the complex-valued hologram under the point light source model. The resulting hologram is then converted to a phase-only hologram using the Floyd-Steinberg dithering algorithm. Second, each phase-only hologram is randomly sampled with the aid of a binary mask. Through the catenation of all selected pixels, a phase-only pixel sequence is formed. Finally, a non-periodic and non-converging sequence generated with the logistic map is used to scramble this sequence. After only preserving the phase data of the scrambled sequence, the real-valued ciphertext carrying the information of all original images is obtained. In the process of authentication, although no valid information can be discerned from noisy reconstructed images at a small sampling rate, the verification of original images can be efficiently accomplished using the nonlinear correlation maps. Besides binary masks, the parameters of the logistic map are served as secret keys. Due to their high sensitivity, the security of the proposed method is greatly enhanced. The proposed authentication mechanism has been demonstrated to be effective and robust through experiments. To our knowledge, it is the first time to implement multiple-image authentication using phase-only holograms, which can provide a new perspective for optical information security.

Optimal Energy Storage Allocation for Combined Wind-PV-EVs-ES System Based on Improved Triangulation Topology Aggregation Optimizer

To determine the ES allocation based on a specific number of EVs connected to a combined WPESS, this paper develops an ESS allocation model that considers the impact of EV charging behavior on LSD, ES allocation cost, new energy utilization rate, and self-power rate. First, several scenarios are generated using Monte Carlo sampling (MCS), and a typical day is selected through Backward Reduction (BR). Next, the Monte Carlo method is employed to generate conventional EV charging curves and optimize EV charging behavior by considering LSD and user charging costs. Subsequently, an ES capacity allocation model is developed, considering system costs, new energy utilization rate, and self-power rate. Finally, an improved triangulation topology aggregation optimizer (TTAO) is proposed, incorporating the logistic map, Golden Sine Algorithm (Gold-SA) strategy, and lens inverse imaging learning strategy. These enhancements improve the algorithm’s ability to identify global optimal solutions and facilitate its escape from local optima, significantly enhancing the optimization effectiveness of TTAO. The analysis of the calculation example indicates that after optimizing the charging behavior of EVs, the average daily cost is reduced by 204.94, the self-power rate increases by 2.25%, and the utilization rate of new energy sources rises by 2.50%, all while maintaining the same ES capacity.

NOVEL TRAIN HEIST OPTIMIZATION AND LOGISTIC CHAOTIC MAP BASED FRESHMAN LEARNING PROCESS INSPIRED ALGORITHM FOR SOLVING THE OPTIMAL POWER FLOW PROBLEM

Train heist based optimization (THO) algorithm is designed based on the really happened train heist in United Kingdom. In the exploration section, robbery gang has been executed the plan has been imitated and mathematically defined. Prior to the execution the robbers plan the conspiracy after multiple examinations on the track. In the exploitation section fled activities of the robbery gang has been emulated and scientifically defined. Even though Leatherslade Farm had been already purchased by the robbery gang, they altered the plan rapidly with minimum stay period in the farm by listening in to the police very high frequencychannels. Chaotic communiqué amongst the gang members and Perception of movement may differ among the gang members and the error value in the decision of the movement is defined. Then in tis paper Logistic chaotic map based freshman learning process inspired optimization (LCP) algorithm is designed to solve the problem. LCP algorithm is designed by imitating the freshman learning process.Trainer will enhance learning processof freshman day by day. Freshman lives in ambiguous world and monetary predicament may originate at dissimilar phases of freshman’s life. Deeds of the freshman learning process are mathematically formulated and population engendered based on the logistic chaos mapping. Trainer will explore the complications and consider a mean point of all complications. Suitable guidance and solutions will be delivered to the freshman by the trainer. Train heist based optimization (THO) algorithm and Logistic chaotic map based freshman learning process inspired optimization (LCP) algorithm are validated in 23 Benchmarking functions and IEEE 30, 354 systems.