Two-dimensional-lag complex logistic map with complex parameters and its encryption application

With the rapid development of internet technology,security protection of information has become more and more prominent,especially information encryption.Considering the great advantages of chaotic encryption,we propose a 2D-lag complex logistic map with complex parameters(2D-LCLMCP)and corresponding encryption schemes.Firstly,we present the model of the 2D-LCLMCP and analyze its chaotic properties and system stability through fixed points,Lyapunov exponent,bifurcation diagram,phase diagram,etc.Secondly,a block cipher algorithm based on the 2D-LCLMCP is proposed,the plaintext data is preprocessed using a pseudorandom sequence generated by the 2D-LCLMCP.Based on the generalized Feistel cipher structure,a round function F is constructed using dynamic S-box and DNA encoding rules as the core of the block cipher algorithm.The generalized Feistel cipher structure consists of two F functions,four XOR operations,and one permutation operation per round.The symmetric dynamic round keys that change with the plaintext are generated by the 2D-LCLMCP.Finally,experimental simulation and performance analysis tests are conducted.The results show that the block cipher algorithm has low complexit,good diffusion and a large key space.When the block length is 64 bits,only six rounds of encryption are required to provide sufficient security and robustness against cryptographic attacks.

Analysis and confirmation of fixed points in logistic mapping digital-flow chaos

The fixed points in logistic mapping digital-flow chaos strange attractor arestudied in detail. When k=n in logistic equation, there exist no more than 2n fixed points, whichare deduced and proved theoretically. Three corollaries about the fixed points of logistic mappingare proposed and proved respectively. These theorem and corollaries provide a theoretical basis forchoosing parameter of chaotic sequences in chaotic secure communication and chaotic digitalwatermarking. And they are testified by simulation.

Hybrid Image Compression-Encryption Scheme Based on Multilayer Stacked Autoencoder and Logistic Map

Secure transmission of images over a communication channel, with limited data transfer capacity, possesses compression and encryption schemes. A deep learning based hybrid image compression-encryption scheme is proposed by combining stacked auto-encoder with the logistic map. The proposed structure of stacked autoencoder has seven multiple layers, and back propagation algorithm is intended to extend vector portrayal of information into lower vector space. The randomly generated key is used to set initial conditions and control parameters of logistic map. Subsequently, compressed image is encrypted by substituting and scrambling of pixel sequences using key stream sequences generated from logistic map.The proposed algorithms are experimentally tested over five standard grayscale images. Compression and encryption efficiency of proposed algorithms are evaluated and analyzed based on peak signal to noise ratio(PSNR), mean square error(MSE), structural similarity index metrics(SSIM) and statistical,differential, entropy analysis respectively. Simulation results show that proposed algorithms provide high quality reconstructed images with excellent levels of security during transmission..

基于logistic map的未来几年成都市人口数量预测

针对近几年成都市人口的迅速增长,运用线性回归分析和数据拟合等构建了logistic map模型,确定了较准确的变化参数r,以预测未来几年成都市的人口数量。综合运用MATLAB和Excel等软件求解,研究认为变化参数r与其所在的年限呈正相关,可以结合近10年来成都市的人口数量推测出未来几年成都市的人口数量。

Bifurcation analysis of the logistic map via two periodic impulsive forces

The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influ- ences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincar6 map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map.

Image Encryption Using Multi-Scroll Attractor and Chaotic Logistic Map

In the current scenario,data transmission over the network is a challenging task as there is a need for protecting sensitive data.Traditional encryption schemes are less sensitive and less complex thus prone to attacks during transmission.It has been observed that an encryption scheme using chaotic theory is more promising due to its non-linear and unpredictable behavior.Hence,proposed a novel hybrid image encryption scheme with multi-scroll attractors and quantum chaos logistic maps(MSA-QCLM).The image data is classified as inter-bits and intra-bits which are permutated separately using multi scroll attractor&quantum logistic maps to generate random keys.To increase the encryption efficiency,a hybrid chaotic technique was performed.Experimentation is performed in a Qiskit simulation tool for various image sets.The simulation results and theoretical analysis show that the proposed method is more efficient than its classical counterpart,and its security is verified by the statistical analysis,keys sensitivity,and keyspace analysis.The Number of changing pixel rate(NPCR)&the Unified averaged changed intensity(UACI)values were observed to be 99.6%&33.4%respectively.Also,entropy oscillates from 7.9 to 7.901 for the different tested encrypted images.The proposed algorithm can resist brute force attacks well,owing to the values of information entropy near the theoretical value of 8.The proposed algorithm has also passed the NIST test(Frequency Monobit test,Run test and DFT test).

Destruction of Spiral Wave Using External Electric Field Modulated by Logistic Map

Evolution of spiral wave generated from the excitable media within the Barkley model is investigated. The external gradient electric field modulated by the logistic map is imposed on the media （along x- and y-axis）. Drift and break up of spiral wave are observed when the amplitude of the electric field is modulated by the chaotic signal from the logistic map, and the whole system could become homogeneous finally and the relevant results are compared when the gradient electric field is modulated by the Lorenz or Rossler chaotic signal.

Adaptive meta-learning extreme learning machine with golden eagle optimization and logistic map for forecasting the incomplete data of solar iradiance

Solar energy has become crucial in producing electrical energy because it is inexhaustible and sustainable.However,its uncertain generation causes problems in power system operation.Therefore,solar irradiance forecasting is significant for suitable controlling power system operation,organizing the transmission expansion planning,and dispatching power system generation.Nonetheless,the forecasting performance can be decreased due to the unfitted prediction model and lacked preprocessing.To deal with mentioned issues,this paper pro-poses Meta-Learning Extreme Learning Machine optimized with Golden Eagle Optimization and Logistic Map(MGEL-ELM)and the Same Datetime Interval Averaged Imputation algorithm(SAME)for improving the fore-casting performance of incomplete solar irradiance time series datasets.Thus,the proposed method is not only imputing incomplete forecasting data but also achieving forecasting accuracy.The experimental result of fore-casting solar irradiance dataset in Thailand indicates that the proposed method can achieve the highest coeffi-cient of determination value up to 0.9307 compared to state-of-the-art models.Furthermore,the proposed method consumes less forecasting time than the deep learning model.

Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Based on some analyses of existing chaotic image encryption frameworks and a new designed three-dimensional improved logistic chaotic map(3D-ILM),an asymmetric image encryption algorithm using public-key Rivest–Shamir–Adleman(RSA)is presented in this paper.In the first stage,a new 3D-ILM is proposed to enhance the chaotic behavior considering analysis of time sequence,Lyapunov exponent,and Shannon entropy.In the second stage,combined with the public key RSA algorithm,a new key acquisition mathematical model(MKA)is constructed to obtain the initial keys for the 3D-ILM.Consequently,the key stream can be produced depending on the plain image for a higher security.Moreover,a novel process model(NPM)for the input of the 3D-ILM is built,which is built to improve the distribution uniformity of the chaotic sequence.In the third stage,to encrypt the plain image,a pre-process by exclusive OR(XOR)operation with a random matrix is applied.Then,the pre-processed image is performed by a permutation for rows,a downward modulo function for adjacent pixels,a permutation for columns,a forward direction XOR addition-modulo diffusion,and a backward direction XOR addition-modulo diffusion to achieve the final cipher image.Moreover,experiments show that the the proposed algorithm has a better performance.Especially,the number of pixels change rate(NPCR)is close to ideal case 99.6094%,with the unified average changing intensity(UACI)close to 33.4634%,and the information entropy(IE)close to 8.

改进型Logistic-Map混沌序列分析

为了进一步提高Logistic-Map混沌序列的互相关性与自相关性,提出了一种改进型的Logistic-Map混沌序列的构造方法。通过Matlab仿真出扩频通信系统,并对改进型Logistic-Map混沌序列的相关性特性进行了分析,并与传统的Logistic-Map混沌序列做了比较。仿真结果表明,改进型Logistic-Map混沌序列与白噪声的统计特性一致,并且该混沌序列具有更为理想的互相关和自相关特性,更加适合作为扩频通信地址码。

A Trick Formula to Illustrate the Period Three Bifurcation Diagram of the Logistic Map

In this paper we develop an algebraic formula in analyzing the bifurcation of the logistic map. Based on this formula, we give a new, short and rigorous proof for the period-3 bifurcation diagram of the logistic map. Therefore, we simplify the work in previous references and improve some insufficiently rigorous slight defects in them.

Anti-integrability for the Logistic Maps

The embedding of the Bernoulli shift into the logistic map x→μx（1 - x） for μ 〉 4 is reinterpreted by the theory of anti-integrability： it is inherited from the anti-integrable limit μ→∞.

On the Periodic Logistic Map

In this paper, the famous logistic map is studied in a new point of view. We study the boundedness and the periodicity of non-autonomous logistic map xn＋1=rnxx（1-xn）, n=0, 1,...,where {rn} is a positive p-periodic sequence. The sufficient conditions are given to support the existence of asymptotically stable and unstable p-periodic orbits. This appears to be the first study of the map with variable parameter r.

并行组合扩频通信中Logistic-Map序列的优选研究

直接序列扩频通信通常选择m序列和gold码作为地址码,但对于并行组合扩频系统其地址码数量少。在分析并行组合扩频系统基础上,研究Logistic-Map混沌扩频序列优选准则。Logistic-Map混沌扩频序列应用在并行组合扩频系统中,仿真结果表明,Logistic-Map混沌扩频序列可以提供数量众多的适于并行组合扩频通信系统的扩频序列族。

Logistic数字混沌序列性能分析

混沌作为一种非线性动态系统中的现象,受到了人们的重视,研究工作者纷纷探索他在通信中的可能应用。讨论了一种广泛研究的离散时间动态系统Logistic Map所产生的数字混沌序列,通过与m序列比较,分析了其白噪声统计特性,并用计算机进行仿真,做了相应的实验数据分析。结果表明数字混沌序列具有较理想的自相关和互相关特性,且数目极大,是CDMA系统中扩频码的优选码型。

Permutation-substitution image encryption scheme based on a modified chaotic map in transform domain

A new chaotic image encryption scheme based on permutation and substitution in the Fourier domain is presented.Fractional Fourier Transform(FRFT)is used before the encryption scheme to get a large degree of randomization.The permutation is achieved by Baker map and the substitution by a key-related-to-plain-image algorithm based on the modified Logistic map.Modification of the Logistic map is developed to increase the space of the encryption key,and hence increase the security.The key of the encryption algorithm dependents on the plain image,and thus,the cipher image is sensitive to both the initial key and the plain image to resist known-plaintext and chosen plaintext attacks.The key space is large and hence the algorithm can effectively resist brute-force attacks.The proposed scheme is examined using different performance evaluation metrics and the results prove that the proposed scheme is highly secure,and it can effectively resist different attacks.

Prediction on Failure Pressure of Pipeline Containing Corrosion Defects Based on ISSA-BPNNModel

Oil and gas pipelines are affected by many factors,such as pipe wall thinning and pipeline rupture.Accurate prediction of failure pressure of oil and gas pipelines can provide technical support for pipeline safety management.Aiming at the shortcomings of the BP Neural Network(BPNN)model,such as low learning efficiency,sensitivity to initial weights,and easy falling into a local optimal state,an Improved Sparrow Search Algorithm(ISSA)is adopted to optimize the initial weights and thresholds of BPNN,and an ISSA-BPNN failure pressure prediction model for corroded pipelines is established.Taking 61 sets of pipelines blasting test data as an example,the prediction model was built and predicted by MATLAB software,and compared with the BPNN model,GA-BPNN model,and SSA-BPNN model.The results show that the MAPE of the ISSA-BPNN model is 3.4177%,and the R2 is 0.9880,both of which are superior to its comparison model.Using the ISSA-BPNN model has high prediction accuracy and stability,and can provide support for pipeline inspection and maintenance.

PERIODIC SOLUTIONS IN ONE-DIMENSIONAL COUPLED MAP LATTICES

It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.

Chaotic system and QR factorization based robust digital image watermarking algorithm

In order to protect copyright of digital images,a new robust digital image watermarking algorithm based on chaotic system and QR factorization was proposed.The host images were firstly divided into blocks with same size,then QR factorization was performed on each block.Pseudorandom circular chain(PCC) generated by logistic mapping(LM) was applied to select the embedding blocks for enhancing the security of the scheme.The first column coefficients in Q matrix of chosen blocks were modified to embed watermarks without causing noticeable artifacts.Watermark extraction procedure was performed without the original cover image.The experimental results demonstrate that the watermarked images have good visual quality and this scheme is better than the existing techniques,especially when the image is attacked by cropping,noise pollution and so on.Analysis and discussion on robustness and security issues were also presented.

Worst-case tolerance analysis on array antenna based on chaos-genetic algorithm

This paper studies the effect of amplitude-phase errors on the antenna performance. Via builting on a worst-case error tolerance model, a simple and practical worst error tolerance analysis based on the chaos-genetic algorithm （CGA） is proposed. The proposed method utilizes chaos to optimize initial population for the genetic algorithm （GA） and introduces chaotic disturbance into the genetic mutation, thereby improving the ability of the GA to search for the global optimum. Numerical simulations demonstrate that the accuracy and stability of the worst-case analysis of the proposed approach are superior to the GA. And the proposed algorithm can be used easily for the error tolerant design of antenna arrays.