Logistic Map Research Articles

Image encryption algorithm based on DNA encoding and CNN

In this study, a novel, more stable, secure, and reliable image encryption model has been introduced. It combines a Convolutional Neural Network (ConvNet/CNN) model with an intertwining logistic map to generate secret keys. Additionally, initial conditions, control parameters, and secret keys are employed by the intertwining logistic map to produce diverse chaotic sequences. Permutation, DNA encoding, diffusion, and bit reversion operations are applied for scrambling and manipulating image pixels. The proposed encryption model was thoroughly examined using various analysis methods such as cropping attack, histogram analysis, key space evaluation, noise attack, information entropy assessment, differential attack, key sensitivity, and correlation coefficient examination. To expand the keyspace and enhance confusion and diffusion in the proposed encryption algorithm, the model employs different subkeys, private keys, and public keys through the Convolutional Neural Network. Furthermore, numerical and perceptual results were compared with the state-of-the-art outcomes to validate the model. Ultimately, the derived results demonstrate that the proposed intertwining logistic map-based image encryption model utilizing Convolutional Neural Network outperforms existing methods. This is due to its significant improvement in information entropy, enhanced randomness, high resistance against differential and statistical attacks, and overall efficiency.

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.

Period Three Cycles of the Logistic Map

The logistic map is famous for its simple definition yet exotic behavior. Among its many fascinating features are its cycles, that is, iterations of the map that return to their starting points. We use a new algebraic approach to identify the value of the growth parameter of the logistic map at which cycles of period three first appear.

A new 2D-HELS hyperchaotic map and its application on image encryption using RNA operation and dynamic confusion

Chaotic systems are commonly being researched for applications in cryptography. In this study, a novel chaotic two-dimensional hyperchaotic exponential adjusted Logistic and sine map (2D-HELS) is derived from the well-known two-dimensional Logistic map and Sine maps. The resulting chaotic system is demonstrated with the help of bifurcation diagram, chaos trajectories, Lyapunov exponent, sample entropy, permutation entropy, and 0–1 test. A new image encryption algorithm (IEA) is proposed utilizing the 2D-HELS to ensure the essential characteristics of a good cryptographic structure “permutation-diffusion”. The IEA utilizes dynamic confusion strategy and RNA operation to achieve a highly secure cipher-image. Theoretical analysis and simulation results are compared with some recently developed cryptosystems. It demonstrates that the 2D-HELS-IEA has splendid achievement in well-known security indicators. Hence, the 2D-HELS-IEA is highly secure as a conclusion.

Short message encryption technology of Beidou communication based on SM9

AbstractTo reduce the security authentication time cost, forwarding delay, and enhance message security of Beidou communication short messages, this paper proposes a Beidou communication short message encryption technology based on SM9 (Mobile Code Secure Communication). This technology uses split hierarchical clustering algorithm to cluster the short message data of Beidou Communication, in order to unify the processing of similar short message data and improve the encryption efficiency of subsequent short messages. Based on the data clustering results, this paper constructs a short message forwarding verification model using the SM9 identification password algorithm, and provides the message content of the communication application protocol and the communication receiving information protocol to achieve low‐cost and efficient forwarding verification. In addition, this article improves the initial value selection of Logistic chaotic mapping by coupling the tent map with coupled mapping lattice (CML) in the spatiotemporal chaos model to generate a chaotic initial value sequence, thereby expanding the key space, enhancing the ability to resist exhaustive attacks, enhancing the randomness of the generated key parameters, and optimizing the encryption effect of short messages. The experimental results show that the short message security authentication time of the technology proposed in this article is basically controlled within 25 ms, and the minimum forwarding delay is only 23.9 ms, which can effectively resist attacks and improve the security of Beidou communication.

A dual image encryption method based on improved Henon mapping and improved Logistic mapping

A dual image encryption method based on improved Henon mapping and improved Logistic mapping

An Improved Harris Hawks Optimization Algorithm for Solving the Permutation Flow Shop Scheduling Problem

In this paper, an improved Harris Hawks optimization algorithm is proposed to solve the permutation flow shop scheduling problem with the objective of minimizing the completion time. Logistic chaotic mapping and inverse learning strategy are used to generate a high-quality initial population. A golden sine algorithm is introduced to improve the position update method. A nonlinear escape energy factor and adaptive t-distribution strategy are introduced to solve the problem of imbalance between the exploration and exploitation phases of the HHO algorithm. The effectiveness of the improved Harris Hawks optimization algorithm is verified by testing it on the Reeves benchmark test set and comparing it with other algorithms.

Analysis of Chaotic Logistic Map used to Generate Secret Keys

Chaotic logistic map is a good model which can be used to generate various secret keys used in data cryptography. In this paper research a detailed analysis of CLM will be introduced. The behavior of CLM will be studied to show how to select the best values of the CLM parameters (growth rate, initial population and the length of the population). Various ranges of the population growth and the initial population will be tested. It will be shown how to use the generated populations to form various secret keys. The sensitivity of CLM will be studied, and it will be shown that any minor changes in the CLM parameters will lead to change the generated population. The population generation time will be tested using various in length generated population, and some recommendation will be provided when dealing with data with big size. It will be shown that using CLM will provide a good security level when using the CLM parameters as a private key.

Hybrid Cryptosystem using Lattice Permutation and Chaos Logistic Mapping for Image Security

Every platform of business uses online services and are increasing. Wired and wireless networks are becoming popular day by day. With this the sensitive data is carried over internet on daily basis. Due to rapid growth of networks, information security becomes more important. Hence, there is every chance of misleading the data by unauthorized parties. So, there is need to provide security for the data and cryptography is the science that helps in providing security. Encryption algorithm plays a crucial role in information security. This paper briefly describes a new hybrid system to enhance security. In this work along with traditional operations Lattice permutation is used in encryption process. For key generation Chaos Logistic Mapping is used that shows more resistance while breaking key by unauthorized persons. Services like online transactions may be largely protected with this type of newly proposed hybrid systems.

Migration time prediction and assessment of toxic fumes under forced ventilation in underground mines

This study aims to predict the migration time of toxic fumes induced by excavation blasting in underground mines. To reduce numerical simulation time and optimize ventilation design, several back propagation neural network (BPNN) models optimized by honey badger algorithm (HBA) with four chaos mapping (CM) functions (i.e., Chebyshev (Che) map, Circle (Cir) map, Logistic (Log) map, and Piecewise (Pie) map) are developed to predict the migration time. 125 simulations by the computational fluid dynamics (CFD) method are used to train and test the developed models. The determination coefficient (R2), the variance accounted for (VAF), the Willmott’s index (WI), the root mean square error (RMSE), the mean absolute percentage error (MAPE), and the sum of squares error (SSE) are utilized to evaluate the model performance. The evaluation results indicate that the CirHBA-BPNN model has achieved the most satisfactory performance by reaching the highest values of R2 (0.9945), WI (0.9986), VAF (99.4811%), and the lowest values of RMSE (15.7600), MAPE (0.0343) and SSE (6209.4), respectively. The wind velocity in roadway (Wv) is the most important feature for predicting the migration time of toxic fumes. Furthermore, the intrinsic response characteristic of the optimal model is implemented to enhance the model interpretability and provide reference for the relationship between features and migration time of toxic fumes in ventilation design.

Research on Dynamic Reactive Power Cost Optimization in Power Systems with DFIG Wind Farms

As the power market system gradually perfects, the increasingly fierce competition not only drives industry development but also brings new challenges. Reactive power optimization is crucial for maintaining stable power grid operation and improving energy efficiency. However, the implementation of plant–grid separation policies has kept optimization costs high, affecting the profit distribution between power generation companies and grid companies. Therefore, researching how to effectively reduce reactive power optimization costs, both technically and strategically, is not only vital for the economic operation of the power system but also key to balancing interests among all parties and promoting the healthy development of the power market. Initially, the study analyzes and compares the characteristic curves of synchronous generators and DFIGs, establishes a reactive power pricing model for generators, and considering the randomness and volatility of wind energy, establishes a DFIG reactive power pricing model. The objective functions aimed to minimize the cost of reactive power purchased by generators, the price of active power network losses, the total deviation of node voltages, and the depreciation costs of discrete variable actions, thereby establishing a dynamic reactive power optimization model for power systems including doubly-fed wind farms. By introducing Logistic chaotic mapping, the CSA is improved by using the highly stochastic characteristics of chaotic systems, which is known as the Chaotic Cuckooing Algorithm. Meanwhile, the basic cuckoo search algorithm was improved in terms of adaptive adjustment strategies and global convergence guidance strategies, resulting in an enhanced cuckoo search algorithm to solve the established dynamic reactive power optimization model, improving global search capability and convergence speed. Finally, using the IEEE 30-bus system as an example and applying the improved chaotic cuckoo search algorithm for solution, simulation results show that the proposed reactive power optimization model and method can reduce reactive power costs and the number of discrete device actions, demonstrating effectiveness and adaptability. When the improved chaotic cuckoo algorithm is applied to optimize the objective function, the optimization result is better than 7.26% compared to the standard cuckoo search algorithm, and it is also improved compared to both the PSO algorithm and the GWO algorithm.

Remote sensing image encryption algorithm utilizing 2D Logistic memristive hyperchaotic map and SHA-512

Remote sensing image encryption algorithm utilizing 2D Logistic memristive hyperchaotic map and SHA-512

IS-DGM: an improved steganography method based on a deep generative model and hyper logistic map encryption via social media networks

IS-DGM: an improved steganography method based on a deep generative model and hyper logistic map encryption via social media networks

A secure data hiding system in biomedical images using grain 128a algorithm, logistic mapping and elliptical curve cryptography

A secure data hiding system in biomedical images using grain 128a algorithm, logistic mapping and elliptical curve cryptography

Secure Multiple-Image Transfer by Hybrid Chaos System: Encryption and Visually Meaningful Images

The secure transmission of information is one of the most important topics in the field of information technology. Considering that images contain important visual information, it is crucial to create a safe platform for image transfer. One commonly employed tool to enhance the complexity and randomness in image encryption methods is the chaos system. The logistic and sine maps are utilized in encryption algorithms but these systems have some weaknesses, notably chaotic behavior in a confined area. In this study, to address these weaknesses, a hybrid system based on the Atangana–Baleanu fractional derivative is proposed. The various tests employed to evaluate the behavior of the new system, including the NIST test, histogram analysis, Lyapunov exponent calculation, and bifurcation diagram, demonstrate the efficiency of the proposed system. Furthermore, in comparison to the logistic and sine maps, the proposed hybrid exhibits chaotic behavior over a broader range. This system is utilized to establish a secure environment for the transmission of multiple images within an encryption algorithm, subsequently concealing them within a meaningful image. Various tools employed to assess the security of the proposed algorithm, including histogram analysis, NPCR, UACI, and correlation values, indicate that the proposed hybrid system has application value in encryption.

S-box design based on logistic skewed chaotic map and modified Rabin-Karp algorithm: applications to multimedia security

A substitution box (S-box) serves as the nonlinearity component in a symmetric key encryption scheme; it directly determines the performance and security level of ciphers. Thus, the construction of an S-box with superior performance and efficiency, specifically in terms of high cryptographic properties, is critical. This research proposes a novel method to construct the S-box using the skewed logistic chaotic map and modified Rabin-Karp rolling hash function without disturbing its mathematical structure. First, iterate the skewed logistic map by selecting a seed value and specifying the parameters to generate the chaotic values. The map’s sensitivity to initial conditions and parameters results in a seemingly random and unpredictable chaotic values. Second, hash the chaotic values using Rabin-Karp for generating sequences of numbers within a specific range (0–255 for an 8-bit S-box). Then an S-box is constructed using the hash values. Performance evaluations indicate that the S-box produced through our suggested approach exhibits superior performance, demonstrating robust resistance against various security threats, including but not limited to linear attacks, differential attacks, and others. To demonstrate the effectiveness of the constructed S-box, this paper goes on to employ it in an image encryption application. Security analyses reveal that the developed image encryption algorithm successfully encrypts diverse types of images, producing cipher images characterized by uniformly distributed histograms. Performance assessments illustrate its high-security level, surpassing several state-of-the-art encryption algorithms.

Simplicity bias, algorithmic probability, and the random logistic map

Simplicity bias is an intriguing phenomenon prevalent in various input–output maps, characterized by a preference for simpler, more regular, or symmetric outputs. Notably, these maps typically feature high-probability outputs with simple patterns, whereas complex patterns are exponentially less probable. This bias has been extensively examined and attributed to principles derived from algorithmic information theory and algorithmic probability. In a significant advancement, it has been demonstrated that the renowned logistic map xk+1=μxk(1−xk), a staple in dynamical systems theory, and other one-dimensional maps exhibit simplicity bias when conceptualized as input–output systems. Building upon this work, our research delves into the manifestations of simplicity bias within the random logistic map, specifically focusing on scenarios involving additive noise. This investigation is driven by the overarching goal of formulating a comprehensive theory for the prediction and analysis of time series.Our primary contributions are multifaceted. We discover that simplicity bias is observable in the random logistic map for specific ranges of μ and noise magnitudes. Additionally, we find that this bias persists even with the introduction of small measurement noise, though it diminishes as noise levels increase. Our studies also revisit the phenomenon of noise-induced chaos, particularly when μ=3.83, revealing its characteristics through complexity-probability plots. Intriguingly, we employ the logistic map to illustrate a paradoxical aspect of data analysis: more data adhering to a consistent trend can occasionally lead to reduced confidence in extrapolation predictions, challenging conventional wisdom.We propose that adopting a probability-complexity perspective in analyzing dynamical systems could significantly enrich statistical learning theories related to series prediction and analysis. This approach not only facilitates a deeper understanding of simplicity bias and its implications but also paves the way for novel methodologies in forecasting complex systems behavior, especially in scenarios dominated by uncertainty and stochasticity.

Systemic cycles of accumulation and chaos in the world capitalist system: a missing link

Abstract We re-examine the systemic cycles of accumulation (SCA) of Arrighi (2010) and Arrighi and Silver (1999) which provide a framework for the analysis of the cyclical patterns of geographical expansion of trade and production and the related shifts of hegemonic power within the world capitalist system. Within the SCA framework, the last stage of a hegemonic cycle is characterized by what is called ‘systemic chaos’. However, the drivers of these dynamics have not been explicitly analyzed. This article fills this gap by providing a link between the accumulation process and systemic chaos. Introducing the logistic map into the SCA analysis, our approach provides the missing detailed understanding of how systemic chaos is an outcome of the contradictory socioeconomic dynamics of capital accumulation itself while being based on the key insights of the SCA framework of hegemonic cycles.

Railway wagon bearing fault diagnosis method based on improved sparrow search algorithm optimizing variational mode decomposition and multi-level convolutional neural network.

Ensuring the safe operation of trains hinges on precise bearing condition monitoring, given the pivotal role bearings play in railway wagons. The status and maintenance of wagon bearings are of paramount concern, necessitating a shift from traditional maintenance approaches reliant on schedules and experience, which often lack real-time precision and efficiency. To address this challenge, our research focuses on enhancing the sparrow search algorithm by incorporating logistic chaos mapping and the levy flight strategy. This enhanced algorithm optimizes variational mode decomposition parameters, utilizing intrinsic mode components' average dispersion entropy as the fitness function. This optimization is integrated with a multi-level convolutional neural network for bearing fault diagnosis. Our findings demonstrate the improved algorithm's enhanced spatial search capabilities and reduced modal aliasing in the frequency components. Experimental validation on public datasets and the group's experimental platform for railway wagons shows that multi-level convolutional neural networks have higher diagnostic accuracy and faster convergence speeds than traditional models such as LeNet-5, AlexNet, and convolutional neural network. Our research introduces a highly accurate and widely applicable methodology for mechanical equipment fault diagnosis, aligning with the requirements of the "smart" era.

An Audio Encryption Scheme Based on Empirical Mode Decomposition and 2D Cosine Logistic Map

An Audio Encryption Scheme Based on Empirical Mode Decomposition and 2D Cosine Logistic Map