Logistic Map Research Articles

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.

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.

Chaotic laser time series prediction based on an improved logistic mapping algorithm echo state network

Chaos synchronization plays vital functions in the fields of optical chaos secure communication. The synchronization performance can be significantly degraded by parameter mismatches between the chaotic transmitter and receiver. In this paper, the Deep-Logistical Mapping Echo State Network (D-LMESN) is proposed to enhance the performance of chaos synchronization. The network is upgraded by using an improved logical mapping algorithm and a deep reserve pool structure with phase space reconstruction. Results show that D-LMESN exhibits better performance in the prediction of chaotic time series, thanks to the adaptive parameter adjustment, which increases the ability to capture the dynamic characteristics of complex systems. Compared with ESN, the mean square error of this model is reduced by 55% and 72%, respectively, in chaotic laser simulation and actual data experiments. This provides a new possibility, to our knowledge, for the development of chaotic secure communication.

A novel 2D Hyperchaotic Sine Logistic map based image encryption scheme

A novel 2D Hyperchaotic Sine Logistic map based image encryption scheme

Heuristic Optimization Algorithm of Black-Winged Kite Fused with Osprey and Its Engineering Application.

Swarm intelligence optimization methods have steadily gained popularity as a solution to multi-objective optimization issues in recent years. Their study has garnered a lot of attention since multi-objective optimization problems have a hard high-dimensional goal space. The black-winged kite optimization algorithm still suffers from the imbalance between global search and local development capabilities, and it is prone to local optimization even though it combines Cauchy mutation to enhance the algorithm's optimization ability. The heuristic optimization algorithm of the black-winged kite fused with osprey (OCBKA), which initializes the population by logistic chaotic mapping and fuses the osprey optimization algorithm to improve the search performance of the algorithm, is proposed as a means of enhancing the search ability of the black-winged kite algorithm (BKA). By using numerical comparisons between the CEC2005 and CEC2021 benchmark functions, along with other swarm intelligence optimization methods and the solutions to three engineering optimization problems, the upgraded strategy's efficacy is confirmed. Based on numerical experiment findings, the revised OCBKA is very competitive because it can handle complicated engineering optimization problems with a high convergence accuracy and quick convergence time when compared to other comparable algorithms.

Chaotic dynamics of a delayed fractional order MLNCML system

Abstract We present a delayed fractional order spatiotemporal dynamical system using the mixed linear-nonlinear coupling connections between lattices. In the simulation experiments, the dynamical characteristics of the proposed model are looked into and analyzed by using bifurcation diagrams and metric entropy density. The proposed model has fewer periodic windows in its bifurcation diagrams, large key space and strong ergodicity due to the delay. These excellent properties are of great significance in encryption. Moreover, the parameter μ breaks its fixed range in the traditional logistic map, which can contribute to enlarge the key space of cryptosystem. Through numerical simulations and security analysis, it is found that the proposed model is applied for encryption.

Stegocrypt: A robust tri‐stage spatial steganography algorithm using TLM encryption and DNA coding for securing digital images

AbstractThis research work presents a novel secured spatial steganography algorithm consisting of three stages. In the first stage, a secret message is divided into three parts, each is encrypted using a tan logistic map encryption key with a unique seed value. In the second stage, the encrypted parts are transformed into quick response codes, serving as a layer of channel coding. Subsequently, the quick response codes are decoded back into bit‐streams. To enhance security, a uniquely‐seeded Mersenne Twister key is generated and employed to apply DNA coding onto each bit‐stream. The resulting bit‐streams are then embedded in the least significant bits of the RGB channels of a cover image. Finally, the RGB channels are merged to form a single stego image. A comprehensive set of experimental analyses is conducted to evaluate the performance of the proposed secure steganography algorithm. The experimental results demonstrate the algorithm's robustness against various attacks and its ability to achieve high embedding capacity while maintaining imperceptibility. The proposed algorithm offers a promising solution for secure information hiding in the spatial domain, with potential applications in areas such as data transmission, digital forensics, and covert communication.

Hybrid Multi-Objective Chameleon Optimization Algorithm Based on Multi-Strategy Fusion and Its Applications.

Aiming at the problems of chameleon swarm algorithm (CSA), such as slow convergence speed, poor robustness, and ease of falling into the local optimum, a multi-strategy improved chameleon optimization algorithm (ICSA) is herein proposed. Firstly, logistic mapping was introduced to initialize the chameleon population to improve the diversity of the initial population. Secondly, in the prey-search stage, the sub-population spiral search strategy was introduced to improve the global search ability and optimization accuracy of the algorithm. Then, considering the blindness of chameleon's eye turning to find prey, the Lévy flight strategy with cosine adaptive weight was combined with greed strategy to enhance the guidance of random exploration in the eyes' rotation stage. Finally, a nonlinear varying weight was introduced to update the chameleon position in the prey-capture stage, and the refraction reverse-learning strategy was used to improve the population activity in the later stage so as to improve the ability of the algorithm to jump out of the local optimum. Eighteen functions in the CEC2005 benchmark test set were selected as an experimental test set, and the performance of ICSA was tested and compared with five other swarm intelligent optimization algorithms. The analysis of the experimental results of 30 independent runs showed that ICSA has stronger convergence performance and optimization ability. Finally, ICSA was applied to the UAV path-planning problem. The simulation results showed that compared with other algorithms, the paths generated by ICSA in different terrain scenarios are shorter and more stable.

Copy-Right protection of color videos using robust watermarking based geometrically invariant moments of fractional orders and logistic sine cosine chaotic map

Copy-Right protection of color videos using robust watermarking based geometrically invariant moments of fractional orders and logistic sine cosine chaotic map

Asymptotic distribution of entropies and Fisher information measure of ordinal patterns with applications

We present the asymptotic distribution of the Rényi and Tsallis/Havrda–Charvát entropies and the Fisher information measure of ordinal patterns embedding their serial correlation. We study the convergence behavior of the asymptotic variance for some types of dynamics and the permutation entropy to the limit distribution. These results lead to tests for comparing the underlying dynamics of two time series. We apply these tests to discriminate uniform white noise, logistic maps with Gaussian noise, fractional Brownian motion, and f−k noise, with k∈{0.5,1,1.5,2,2.5}. We also applied these tests to cryptocurrency open prices data, with favorable results. We provide the R code that implements the functions.