Iterative Chaotic Map With Infinite Collapse Research Articles

An Improved Binary Walrus Optimizer with Golden Sine Disturbance and Population Regeneration Mechanism to Solve Feature Selection Problems.

Feature selection (FS) is a significant dimensionality reduction technique in machine learning and data mining that is adept at managing high-dimensional data efficiently and enhancing model performance. Metaheuristic algorithms have become one of the most promising solutions in FS owing to their powerful search capabilities as well as their performance. In this paper, the novel improved binary walrus optimizer (WO) algorithm utilizing the golden sine strategy, elite opposition-based learning (EOBL), and population regeneration mechanism (BGEPWO) is proposed for FS. First, the population is initialized using an iterative chaotic map with infinite collapses (ICMIC) chaotic map to improve the diversity. Second, a safe signal is obtained by introducing an adaptive operator to enhance the stability of the WO and optimize the trade-off between exploration and exploitation of the algorithm. Third, BGEPWO innovatively designs a population regeneration mechanism to continuously eliminate hopeless individuals and generate new promising ones, which keeps the population moving toward the optimal solution and accelerates the convergence process. Fourth, EOBL is used to guide the escape behavior of the walrus to expand the search range. Finally, the golden sine strategy is utilized for perturbing the population in the late iteration to improve the algorithm's capacity to evade local optima. The BGEPWO algorithm underwent evaluation on 21 datasets of different sizes and was compared with the BWO algorithm and 10 other representative optimization algorithms. The experimental results demonstrate that BGEPWO outperforms these competing algorithms in terms of fitness value, number of selected features, and F1-score in most datasets. The proposed algorithm achieves higher accuracy, better feature reduction ability, and stronger convergence by increasing population diversity, continuously balancing exploration and exploitation processes and effectively escaping local optimal traps.

An improved mountain gazelle optimizer based on chaotic map and spiral disturbance for medical feature selection.

Feature selection is an important solution for dealing with high-dimensional data in the fields of machine learning and data mining. In this paper, we present an improved mountain gazelle optimizer (IMGO) based on the newly proposed mountain gazelle optimizer (MGO) and design a binary version of IMGO (BIMGO) to solve the feature selection problem for medical data. First, the gazelle population is initialized using iterative chaotic map with infinite collapses (ICMIC) mapping, which increases the diversity of the population. Second, a nonlinear control factor is introduced to balance the exploration and exploitation components of the algorithm. Individuals in the population are perturbed using a spiral perturbation mechanism to enhance the local search capability of the algorithm. Finally, a neighborhood search strategy is used for the optimal individuals to enhance the exploitation and convergence capabilities of the algorithm. The superior ability of the IMGO algorithm to solve continuous problems is demonstrated on 23 benchmark datasets. Then, BIMGO is evaluated on 16 medical datasets of different dimensions and compared with 8 well-known metaheuristic algorithms. The experimental results indicate that BIMGO outperforms the competing algorithms in terms of the fitness value, number of selected features and sensitivity. In addition, the statistical results of the experiments demonstrate the significantly superior ability of BIMGO to select the most effective features in medical datasets.

Medical image encryption system based on a simultaneous permutation and diffusion framework utilizing a new chaotic map

In telemedicine, diverse medical images transmitted between doctors and patients contain sensitive personal information. Thus, there is an urgent need for reliable and efficient medical image encryption to protect these medical images during transmission. In this paper, a simultaneous permutation and diffusion framework (SPDF) is introduced for medical image encryption based on a new chaotic map. Firstly, combining the Chebyshev map and the iterative chaotic map with infinite collapse (ICMIC), we propose a one-dimensional chaotic system (1D-CICMIC) which exhibits higher ergodicity and unpredictability compared to other 1D chaotic maps through comprehensive analyses. Secondly, in order to enhance permutation effect, we modify traditional Josephus traversing with a dynamic scrambling method where the scrambling scheme of the current pixel depends on the value of the previous diffused pixel. Thirdly, we develop a simultaneous permutation and diffusion framework, wherein the diffusion is embedded into the modified Josephus traversing to prevent attackers from targeting the scrambling and diffusion phases separately. Finally, based on 1D-CICMIC and SPDF, an encryption system is proposed. It adopts plaintext correlation in the diffusion operation, which strikes a balance between ciphertext sensitivity and plaintext sensitivity, offering resistance against chosen-plaintext attack (CPA), noise attack and data loss. Simulation results show that the proposed algorithm has high encryption efficiency and can withstand various common attacks.

Multi‐mode non‐linear inversion of Rayleigh wave dispersion curves with grey wolf optimization and cuckoo search algorithm

AbstractDispersion curve inversion is one of the core contents of Rayleigh wave data processing. However, the dispersion curve inversion has the characteristics of multi‐parameter, multi‐extremum as well as nonlinearity. In the face of Rayleigh wave data processing under complex seismic‐geological conditions, it is difficult to reconstruct an underground structure quickly and accurately apply a single global‐searching non‐linear inversion algorithm. For this reason, we proposed a strategy to invert multi‐order mode Rayleigh wave dispersion curves by combining with grey wolf optimization (GWO) and cuckoo search (CS) algorithms. On the basis of introducing the mechanism of iterative chaotic map with infinite collapses (ICMIC) and the strategy of dimension learning–based hunting (DLH), an improved GWO was developed that was called IDGWO (ICMIC and DLH GWO). After searching the near‐optimal region through IDGWO, the CS with a variable step‐size Lévy flight search mechanism was switched adaptively to complete the final inversion. The correctness of our method was verified by the multi‐order mode dispersion curve inversion of a six‐layer high‐velocity interlayer model. Then it was further applied to the processing of real seismic datasets. The research results show that our method fully utilizes the advantages of each of the two global‐searching non‐linear algorithms after integrating IDGWO and CS, while effectively balancing the ability between global search and local exploitation, further improving the convergence speed and inversion accuracy and having good anti‐noise performance.

The New Four-Dimensional Fractional Chaotic Map with Constant and Variable-Order: Chaos, Control and Synchronization

Using fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) with fractional-order. Also, it presents a novel variable-order version of SF-SIMM and discusses their chaotic dynamic behavior by employing a distinct function for the variable fractional-order. To establish the existence of chaos in the suggested discrete SF-SIMM, some numerical methods such as phase plots, bifurcation and largest Lyapunov exponent diagrams, C0 complexity and 0–1 test are utilized. After that, two different control schemes are used for the conceived discrete system. The states are stabilized and asymptotically forced towards zero by the first controller. The second controller is used to synchronize a pair of maps with non–identical parameters. Finally, MATLAB simulations will be executed to confirm the results provided.

A class of m-dimension grid multi-cavity hyperchaotic maps and its application

In this paper, a new closed-loop multiple modulation coupling (CMMC) method is proposed to construct an enhanced chaotic system. Based on the iterative chaotic map with infinite collapse (ICMIC) and Sinusoidal map, a class of hyperchaotic maps are constructed, and a new 3D-Hourglass chaotic map is proposed. Dynamics analyses show that the proposed systems have 3 positive Lyapunov exponents (LEs), large maximum Lyapunov exponents (MLE) and parameter space, good randomness, and high permutation entropy (PE) complexity. Interestingly, the original system exists lots of multiple coexistence attractor rings. In addition, the grid multi-cavity chaotic model of 3D-Hourglass is designed by using nonlinear hyperbolic tangent function, which significantly expands the phase space, and makes the translation control of the cavity smoother. Multi-cavity hyperchaotic map maintains the high complexity and rich dynamics of the original system. Finally, we implement it on DSP, and design Pseudorandom Number Generator (PRNG) as its applications.

VLSI Implementation of Optimized 2D SIMM Chaotic Map for Image Encryption

The current research work proposed a novel optimization-based 2D-SIMM (Two-Dimensional Sine Iterative chaotic map with infinite collapse Modulation Map) model for image encryption. The proposed 2D-SIMM model is derived out of sine map and Iterative Chaotic Map with Infinite Collapse (ICMIC). In this technique, scrambling effect is achieved with the help of Chaotic Shift Transform (CST). Chaotic Shift Transform is used to change the value of pixels in the input image while the substituted value is cyclically shifted according to the chaotic sequence generated by 2D-SIMM model. These chaotic sequences, generated using 2D-SIMM model, are sensitive to initial conditions. In the proposed algorithm, these initial conditions are optimized using JAYA optimization algorithm. Correlation coefficient and entropy are considered as fitness functions in this study to evaluate the best solution for initial conditions. The simulation results clearly shows that the proposed algorithm achieved a better performance over existing algorithms. In addition, the VLSI implementation of the proposed algorithm was also carried out using Xilinx system generator. With optimization, the correlation coefficient was −0.014096 and without optimization, it was 0.002585.

An Efficient Chaos-Based Image Encryption Technique Using Bitplane Decay and Genetic Operators.

Social networks have greatly expanded in the last ten years the need for sharing multimedia data. However, on open networks such as the Internet, where security is frequently compromised, it is simple for eavesdroppers to approach the actual contents without much difficulty. Researchers have created a variety of encryption methods to strengthen the security of this transmission and make it difficult for eavesdroppers to get genuine data. However, these conventional approaches increase computing costs and communication overhead and do not offer protection against fresh threats. The problems with current algorithms encourage academics to further investigate the subject and suggest new algorithms that are more effective than current methods, that reduce overhead, and which are equipped with features needed by next-generation multimedia networks. In this paper, a genetic operator-based encryption method for multimedia security is proposed. It has been noted that the proposed algorithm produces improved key strength results. The investigations using attacks on data loss, differential assaults, statistical attacks, and brute force attacks show that the encryption technique suggested has improved security performance. It focuses on two techniques, bitplane slicing and followed by block segmentation and scrambling. The suggested method first divides the plaintext picture into several blocks, which is then followed by block swapping done by the genetic operator used to combine the genetic information of two different images to generate new offspring. The key stream is produced from an iterative chaotic map with infinite collapse (ICMIC). Based on a close-loop modulation coupling (CMC) approach, a three-dimensional hyperchaotic ICMIC modulation map is proposed. By using a hybrid model of multidirectional circular permutation with this map, a brand-new colour image encryption algorithm is created. In this approach, a multidirectional circular permutation is used to disrupt the image’s pixel placements, and genetic operations are used to replace the pixel values. According to simulation findings and security research, the technique can fend off brute-force, statistical, differential, known-plaintext, and chosen-plaintext assaults, and has a strong key sensitivity.

Intelligent diagnosis of natural gas pipeline defects using improved flower pollination algorithm and artificial neural network

With the increasing service life of pipelines, natural gas pipelines can gradually age and produce various corrosion defects. Hence, in order to ensure the efficiency and safety of pipeline transportation in the peak period of natural gas consumption, the intelligent diagnosis technology of the pipelines is of vital importance. In this paper, iterative chaotic map with infinite collapses (ICMIC) and comprehensive opposition (CO) learning strategy are used to optimize flower pollination algorithm (FPA) to enhance search abilities of original FPA algorithm. Among them, the ICMIC enhances the diversity of population, and the local CO learning strategy enhances its exploitation ability. Fifteen classical benchmark functions are used to test the optimization performance of the improved flower pollination algorithm (IFPA). Considering the category, complexity and application of test functions, a more reasonable evaluation formula is proposed. The test shows that the performance of IFPA algorithm is obviously better than other classical intelligent algorithms. Based on the excellent performance of IFPA, the IFPA algorithm is used to optimize the initial weights and thresholds of back propagation (BP) neural network. Therefore, a comprehensive IFPA-BP network model is constructed for the intelligent diagnosis of natural gas pipeline defects. The results show that the proposed model can effectively overcome the problem that BP neural network is prone to fall into local optimal value, and it can accurately identify the pipelines defects. This will facilitate intelligent diagnosis of natural gas pipelines defects.

A class of higher-dimensional hyperchaotic maps

Based on the hybrid modulation coupling (HMC) pattern, a class of higher-dimensional (HD) hyperchaotic maps is proposed using three one-dimensional (1D) seed maps. The seed maps are chaotic maps or the combination of chaotic maps and non-chaotic maps. Taking the HMC of iterative chaotic map with infinite collapse (ICMIC), Sine map and a linear map (ISL-HMC) as an example, the equilibrium points are mathematically analyzed. The dynamical performance of the 3D ISL-HMC map is evaluated by phase diagram, Lyapunov exponents (LEs), bifurcation diagram and chaos diagram. Furthermore, compared with existing chaotic maps, complexity and distribution characteristic are analyzed. As application of the ISL-HMC map, a pseudorandom number generator (PRNG) is designed and tested by NIST SP 800-22 and TestU01. Experimental results show that the ISL-HMC map has rich dynamical behaviors and good randomness. So this class of HD hyperchaotic maps is a potential model for cryptography and other applications.

A fast image encryption algorithm based on compressive sensing and hyperchaotic map

In this paper, we propose a new two-dimensional Sine improved Logistic iterative chaotic map with infinite collapse (ICMIC) modulation map (2D-SLIM) based on the improved two-dimensional closed-loop modulation coupling model. The performance analysis results show that it has a large parameter space, large Lyapunov exponents and high complexity. Combining this map with compressive sensing, a fast image encryption algorithm is proposed. In this algorithm, a plain image is measured by two circular measurement matrices from two directions, and then the image is re-encrypted by employing the row and column encryption to simultaneously achieve permutation and diffusion. In addition, the SHA-512 hash values of the plain image are generated to calculate the initial conditions of the chaotic map with secret keys, which greatly improve the ability to withstand the known plaintext and chosen plaintext attacks. Simulation and performance analysis verify that this algorithm has acceptable compression, high security and low time complexity.

Designing an M-dimensional nonlinear model for producing hyperchaos

This paper proposes an M-dimensional nonlinear hyperchaotic model (M-NHM) for producing new discrete-time systems with complex hyperchaotic behaviors. The M-NHM is constructed by designing an M-dimensional nonlinear system (M ≥ 2) to generate a chaotic behavior. To enhance the nonlinearity of M-NHM, hence changing its behavior to hyperchaotic, an iterative chaotic map with infinite collapse (ICMIC) is composed. Mathematical analysis shows that the M-NHM has either no equilibria, or an arbitrarily large number of equilibria. Moreover, Routh−Hurwitz criterion reveals that all these equilibria are unstable when M ≥ 3. To investigate the dynamical properties and complexity of the M-NHM, we provide 2-NHM and 3-NHM as typical examples. Simulation results show that the 2-NHM and 3-NHM have good ergodicity, wide hyperchaotic behavior, highly sensitivity dependence, and high complexity. With all these features, the M-NHM would be an ideal model for secure communications and other engineering applications.

Chaotic image encryption scheme using two-by-two deoxyribonucleic acid complementary rules

An image encryption technique has been proposed using deoxyribonucleic acid (DNA) operations and chaotic map in this scheme. First, initial conditions of row encryption and column encryption are calculated. Then, a two-dimensional sine iterative chaotic map with infinite collapse (ICMIC) modulation map (2D-SIMM) is adopted to produce chaotic sequences. Extended exclusive OR (XOR) is executed to enhance security. A mask matrix is produced by 2D-SIMM. It performs XOR operation with the DNA-encoded matrix. Finally, the revised DNA-encoded matrix is performed two-by-two DNA complementary rules and executed DNA decoding to obtain the cipher image. Experiment results prove that the proposed scheme is secure enough and can resist various attacks.

Color Image Encryption Using Three-Dimensional Sine ICMIC Modulation Map and DNA Sequence Operations

Derived from Sine map and iterative chaotic map with infinite collapse (ICMIC), a three-dimensional hyperchaotic Sine ICMIC modulation map (3D-SIMM) is proposed based on a close-loop modulation coupling (CMC) method. Based on this map, a novel color image encryption algorithm is designed by employing a hybrid model of multidirectional circular permutation and deoxyribonucleic acid (DNA) masking. In this scheme, the pixel positions of image are scrambled by multidirectional circular permutation, and the pixel values are substituted by DNA sequence operations. The simulation results and security analysis show that the algorithm has good encryption effect and strong key sensitivity, and can resist brute-force, statistical, differential, known-plaintext and chosen-plaintext attacks.

SF-SIMM high-dimensional hyperchaotic map and its performance analysis

Derived from Sine map and an iterative chaotic map with infinite collapse (ICMIC), a new high-dimensional hyperchaotic map, sinusoidal feedback Sine ICMIC modulation map (SF-SIMM), is proposed. Two-dimensional (2D) model of SF-SIMM is investigated as an example, and its chaotic performances are evaluated. Results show that it has complicated phase space trajectory, infinite equilibrium points, hyperchaotic behaviors, rather large maximum Lyapunov exponent, three typical bifurcations and multiple coexisting attractors with odd symmetry. Furthermore, it has advantages in complexity, distribution characteristics and zero correlation and can generate two independent pseudo-random sequences simultaneously. Therefore, it has good application prospects in secure communication.

A fast image encryption algorithm based on chaotic map

Derived from Sine map and iterative chaotic map with infinite collapse (ICMIC), a new two-dimensional Sine ICMIC modulation map (2D-SIMM) is proposed based on a close-loop modulation coupling (CMC) model, and its chaotic performance is analyzed by means of phase diagram, Lyapunov exponent spectrum and complexity. It shows that this map has good ergodicity, hyperchaotic behavior, large maximum Lyapunov exponent and high complexity. Based on this map, a fast image encryption algorithm is proposed. In this algorithm, the confusion and diffusion processes are combined for one stage. Chaotic shift transform (CST) is proposed to efficiently change the image pixel positions, and the row and column substitutions are applied to scramble the pixel values simultaneously. The simulation and analysis results show that this algorithm has high security, low time complexity, and the abilities of resisting statistical analysis, differential, brute-force, known-plaintext and chosen-plaintext attacks.

A novel chaotic particle swarm optimization based fuzzy clustering algorithm

Clustering is a popular data analysis and data mining technique. In this paper, a novel chaotic particle swarm fuzzy clustering (CPSFC) algorithm based on chaotic particle swarm (CPSO) and gradient method is proposed. Fuzzy clustering model optimization is challenging, in order to solve this problem, adaptive inertia weight factor (AIWF) and iterative chaotic map with infinite collapses (ICMIC) are introduced, and a new CPSO algorithm combined AIWF and ICMIC based chaotic local search is studied. The CPSFC algorithm utilizes CPSO to search the fuzzy clustering model, exploiting the searching capability of fuzzy c-means (FCM) and avoiding its major limitation of getting stuck at locally optimal values. Meanwhile, gradient operator is adopted to accelerate convergence of the proposed algorithm. Its superiority over the FCM algorithm and another two global optimization algorithm-based clustering methods is extensively demonstrated for several artificial and real life data sets in comparative experiments.