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In recent years, many image encryption schemes have adopted Hilbert curves for encryption. In this approach, the Hilbert curve is used to encrypt grayscale images by traversal scrambling. However, the correlation between pixels has not been fully considered and those algorithms are not safe enough. To solve this problem, a new image encryption algorithm based on a new chaotic system of 2D-LICM (Two-Dimensional Linear-Infinite-Collapse Chaotic Map) and an improved Hilbert curve is proposed in this paper. First, we propose a new 2D-chaotic system to address the shortcoming that the commonly used chaotic systems are too simple in scope and complexity. Then, a new image encryption algorithm is proposed using the newly designed 2D-LICM and the improved Hilbert curve. The proposed algorithm uses Hilbert curve to reduce the correlation between adjacent pixels of the image at the pixel and bit levels and increase the scrambling and diffusion effects. Simulation and security analysis results show that the proposed scheme has high security and is superior to several advanced image encryption algorithms. [ABSTRACT FROM AUTHOR]

As digital communication and storage continue to expand, the protection of image privacy information becomes increasingly critical. To safeguard sensitive visual information from unauthorized access, this paper proposes a novel image encryption scheme that integrates multiobjective Artificial Bee Colony (ABC) optimization algorithm and DNA coding. Multiple evaluation metrics including correlation relationship, Number of Pixel Change Rate (NPCR), Unified Average Changing Intensity (UACI), and information entropy are collaboratively optimized by the ABC algorithm. The proposed method begins with the application of the SHA-256 algorithm to generate keys and random sequences using chaotic systems. These sequences are then employed for shuffling, DNA coding, decoding, and diffusion, generating initial encrypted images. Subsequently, the encrypted images serve as individuals within the ABC algorithm to determine optimal parameters of the chaotic systems and the best ciphertext image. Simulation experiments demonstrate that the ciphertext images achieved excellent results in information entropy, pixel correlation coefficient, NPCR, and UACI. The integration of the multiobjective ABC optimization algorithm with DNA coding in our proposed image encryption scheme results in heightened security, as evidenced by superior performance in various metrics. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic multiple-image encryption algorithm using block scrambling and dynamic DNA coding is designed. The algorithm can achieve simultaneous encryption of many different types of images. Firstly, a new block scrambling algorithm is proposed, which is divided into two scrambling modes according to the size of the initial block. And it combines with the cyclic shift operation to achieve scrambling. Secondly, dynamic DNA coding is utilized to diffuse images, which enhances the complexity and security of the proposed multiple-image encryption algorithm. Through the analysis of key space, correlation, information entropy, histogram, differential attacks and robustness, it is verified that the algorithm is safe and effective. Experimental results show that the new multiple-image encryption algorithm is suitable for multiple color and gray images encryption. The algorithm has excellent encryption performance, and can be applied in secure communication. [ABSTRACT FROM AUTHOR]

Recently, a chaotic secure video communication system based on FPGA is proposed, which essentially encrypts the original image data of each frame in the video in multiple rounds by using the 6D self-synchronizing chaotic stream cipher. In this paper, the security performance of the multiround encryption algorithm is analyzed based on divide-and-conquer attack. In the case of one round encryption, the keys ψ i j (1 ≤ i ≤ 3 , 1 ≤ j ≤ 6) can be deciphered by setting 30 appropriate initial conditions according to known-plaintext attack. After that, according to chosen-ciphertext attack, the chaotic iterative equation of the decryption end is degenerated into a linear one if ciphertexts are all set to zero. Under this condition, the equations between the unknown keys and the plaintext-ciphertext pairs can be obtained by setting 24 appropriate initial conditions, and the keys ψ i j (4 ≤ i ≤ 6 , 4 ≤ j ≤ 6) can be deciphered by solving the equations in Mathematica. Secondly, in order to reduce the multiplication times of the unknown keys in the case of two-round encryption, the number of pixels in an image can be selected as little as possible. According to chosen-ciphertext attack, when the number of the pixels in an image is only one, the keys ψ i j (1 ≤ i ≤ 3 , 1 ≤ j ≤ 6) can be deciphered by setting 30 appropriate initial conditions. Then, when the number of pixels in an image is two, the keys ψ i j (4 ≤ i ≤ 6 , 4 ≤ j ≤ 6) can be deciphered by setting 24 appropriate initial conditions. However, in the case that the encryption round is three or more, the keys cannot be deciphered by the attack method proposed in this paper. The analysis results show that the multiround image encryption algorithm is not secure when the number of encryption rounds is one or two. [ABSTRACT FROM AUTHOR]

Since the current general image encryption algorithms based on chaotic systems and classical permutation diffusion structures typically suffer from stochastic degradation, simple algorithm structures, and reduced execution efficiency when dealing with images with large data, this paper proposes a new multiprocess image encryption algorithm based on a new hyperchaotic coupled sine map. To begin with, by performing dynamic analyses of the map, including equilibrium points, bifurcation diagrams, Lyapunov exponent diagrams, and phase diagrams, associated performance analyses show high spectral entropy (SE) values and permutation entropy (PE) values. Meanwhile, sequences generated by the proposed map are able to pass the NIST randomness test, which shows its suitability for the design of encryption algorithms. Then, a chaos-based image encryption algorithm is proposed in this paper: In the preprocessing stage, the images are sparsely sampled using a compressed-sensing method; in the permutation stage, the image is decomposed into eight bit-plane images containing only 0s and 1s and a clockwise cyclic shift operation based on a chaotic sequence is applied in each bit-plane image to achieve a bit-level permutation effect; in the diffusion stage, the block DNA random computing is applied to the permuted image to modify the pixel values and the final cipher image is obtained. In addition, the initial value of the map is determined by the preset initial value, user-defined strings, and the Hash value of the plain image, where the Hash value of the plain image is calculated by the SHA-256 algorithm. Finally, the analysis of the algorithm demonstrates that the algorithm exhibits extremely strong plaintext correlation externally and excellent encryption performance in terms of attack resistance and execution efficiency. [ABSTRACT FROM AUTHOR]

This paper proposes a new chaotic system 2D-HLM, which is a combination of Henon map and logistic map. SHA-256 algorithm based on the plaintext image produces the initial value, which enhances the correlation with the plaintext. Therefore, the algorithm avoids the disadvantages of being easily cracked by selected plaintext attacks. The chaotic sequence generated by 2D-HLM is adopted to scramble an image, and the bit plane is extracted and reorganized on the scrambled image. Based on the relationship between two mathematical propositions of the logistic map operations, a novel propositional logic coding algorithm is proposed. The simulation results show that the algorithm has large key space and high key sensitivity, and can resist common attacks such as differential attack. [ABSTRACT FROM AUTHOR]

In the field of secure communications, the robustness of cipher images transmitted in various channels is becoming increasingly important. In this paper, a robust image encryption algorithm combining a new chaotic system and discrete cosine transform is proposed, which is interlinked with plain information and is resistant to high-intensity noise attacks. First, a 5D continuous hyperchaotic system is proposed, leading to an interrelated sequence of five chaotic sequences. Second, the plain image is subjected to discrete cosine transform. Then the transform domain image is quantized, and some high-frequency components are removed, and then the high-frequency components are filled with chaotic sequences. Next, the transform domain image is scrambled, and inverse discrete cosine transform is performed, and its gray value is mapped to obtain a spatial domain image. Finally, the spatial image is scrambled by the spiral transformation, and then the diffusion operation is performed to obtain the encrypted image. Through the simulation experiment, the histogram, correlation, differential attack, and robustness are analyzed. The experimental results show that the proposed encryption algorithm can resist high-intensity noise attacks and has good encryption performance. [ABSTRACT FROM AUTHOR]

In this paper, a new 4D chaos system is introduced based on the mathematical structure through composing and transferring. The behavior of the proposed chaotic system is studied using different tests, such as Lyapunov exponent, bifurcation diagram and histogram. In order to show the advantage of the new chaos system, the proposed system is used for image encryption. In the proposed algorithm, in addition to the new chaos system, cellular automata is also used to improve the security of the algorithm. The proposed algorithm has a separate structure for encryption key, which increases the security of the proposed algorithm. The security of the proposed environment which is evaluated using different types of security tests shows the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper introduces a novel hyperchaotic circuit system that is extremely sensitive to circuit parameters and system initial values. The typical dynamical behaviors of the hyperchaotic system such as one-parameter bifurcation diagrams, two-parameter bifurcation diagrams and Lyapunov exponent spectrum are discussed in detail. Then an image encryption algorithm is designed by using the hyperchaotic sequences. In this algorithm, Zigzag algorithm is used to scramble pixel positions, and backward diffusion and forward diffusion algorithms are used to diffuse pixel values. The results indicate that the proposed algorithm can improve the security of the image encryption algorithm. In addition, some circuit simulation experiments are performed to verify the sensitivity of the hyperchaotic circuit to parameters by Multisim. Finally, the hyperchaotic circuit is implemented by using physical elements. The simulation results are consistent with the experimental results of hardware circuit, which effectively verifies the existence of hyperchaotic attractors. [ABSTRACT FROM AUTHOR]

In this paper, the Benettin–Wolf algorithm for determining all Lyapunov exponents of noncommensurate fractional-order systems modeled by Caputo's derivative and the corresponding Matlab code are presented. The paper continues the work started in [Danca & Kuznetsov, 2018], where the Matlab code of commensurate fractional-order systems is given. To integrate the extended systems, the Adams–Bashforth–Moulton scheme for fractional differential equations is utilized. Like the Matlab program for commensurate-order systems, the program presented in this paper prints and plots all Lyapunov exponents as function of time. The program can be simply adapted to plot the evolution of the Lyapunov exponents as a function of orders, or a function of a bifurcation parameter. Special attention is paid to the periodicity of fractional-order systems and its influences. The case of noncommensurate Lorenz system is demonstrated. [ABSTRACT FROM AUTHOR]

An intrinsic similarity was noted between epidemic spreading models and diffusion operations in cryptography. In this paper, a new image encryption algorithm is proposed based on an epidemic spreading model. The notable feature of the model is the evolution of the network node state. We utilize the evolution of an epidemic spreading model, namely the susceptible-infectious-recovered (SIR) model, to drive the encryption progress by abstracting pixels to the network nodes. In the new cryptosystem, the pixels in plain-text are considered as susceptible individuals, permutation and diffusion are seamlessly integrated rather than having two independent stages, and the encryptions are performed in a two-dimensional and nonlinear manner. Simulation results demonstrate its high encryption speed and excellent encryption security. [ABSTRACT FROM AUTHOR]

Saddle fixed points are the centerpieces of complicated dynamics in a system. The one-dimensional stable and unstable manifolds of these saddle-points are crucial to understanding the dynamics of such systems. While the problem of sketching the unstable manifold is simple, plotting the stable manifold is not as easy. Several algorithms exist to compute the stable manifold of saddle-points, but they have their limitations, especially when the system is not invertible. In this paper, we present a new algorithm to compute the stable manifold of two-dimensional systems which can also be used for noninvertible systems. After outlining the logic of the algorithm, we demonstrate the output of the algorithm on several examples. [ABSTRACT FROM AUTHOR]

The key expansion algorithm is an important part of a general iterated block cipher, because its security determines the security level of the encryption scheme. Thus, generating secure round keys with statistical independence and sensitivity is desirable. An irreversible parallel key expansion algorithm is proposed based on a chaotic map in this paper. First, an enhanced nondegenerate 2D exponential chaotic map (2D-ECM) with ergodicity is constructed, with analysis results demonstrating that it has better dynamical characteristics. Then, an irreversible key expansion algorithm is designed based on the 2D-ECM, which has high sensitivity to initial key with independence between round keys. Experimental results and performance analysis demonstrate that the algorithm is feasible and can resist the side channel power attack. [ABSTRACT FROM AUTHOR]

To improve the security level of image encryption based on chaos theory, a novel bit-level transform method which could enhance the dynamical performance of chaotic maps is proposed and a new image encryption algorithm based on a random irregular blocking method is also designed in this paper. Firstly, in the bit-level transform method, three chaotic maps are combined to generate a novel chaotic sequence. From a series of performance analyses results, the generated sequence not only successfully passes NIST tests, but also performs better than the original sequence, with a larger chaotic parametrial range, high complexity, etc. Then, an image encryption algorithm based on the newly generated chaotic sequence is proposed, in which a random irregular blocking method is adopted. Random irregular blocking could solve the problem of insecurity in the fixed blocking method. With a color Lena image as an encryption example, we analyze the security of the encryption algorithm by conducting a sufficiently large number of experiments using the encrypted image. For the encrypted Lena image, the average values of information entropy, NPCR, and UACI are 7.9931, 0.9961, and 0.3352, respectively. The experimental results and security analyses results provide evidence that the proposed encryption algorithm has good performance and can resist various typical attacks. [ABSTRACT FROM AUTHOR]

Based on the dispersion entropy model, combined with multiscale analysis method and fractional order information entropy theory, this paper proposes new models — the generalized fractional order multiscale dispersion entropy (GMDE) and the generalized fractional order refined composite multiscale dispersion entropy (GRCMDE). The new models take the amplitude value information of the sequence itself into consideration, which can make better use of some key information in the sequence and have a higher stability and accuracy. In addition, extending the algorithm to generalized fractional order can make the model better capture the small evolution of the signal data, which is more advantageous for studying the dynamic characteristics of complex systems. This paper verifies the effectiveness of the new models by combining theoretical analysis with empirical research, and further studies the complexity of the financial system and the nature of its multiple time scales. The results show that the proposed GMDE, GRCMDE can better detect the intrinsic nature of financial time series and can distinguish the financial market complexity of different countries. [ABSTRACT FROM AUTHOR]

In recent years, image encryption schemes based on optical methods have been extensively studied. However, possible optical encryption methods in combination with fractional-order laser hyperchaotic systems have not been reported. Therefore, an optical image encryption scheme based on fractional Fourier transform and five-dimensional host-induced nonlinearity fractional-order laser hyperchaotic system is studied in this paper. Firstly, the dynamical characteristics of the proposed fractional-order laser hyperchaotic system are analyzed, and the DSP platform is used to realize the system. Then, a novel image encryption scheme is proposed combining BP neural network, GF(17) domain diffusion and hyperchaotic, random point scrambling algorithm. Finally, the performance of the encryption scheme is analyzed in detail. This work provides an experimental basis and theoretical guidance for image secure communication combining fractional-order laser hyperchaotic systems and optical methods and offers a new research perspective for optical image encryption. [ABSTRACT FROM AUTHOR]

Chaotic maps have been widely used in image encryption due to their complexity, pseudorandomness and high sensitivity to initial values. In this paper, an image encryption algorithm based on a 4D chaotic map and steganography is proposed. The algorithm consists of two rounds of encryption and one operation of embedding hash. In the first round of encryption, the hash value of plaintext image is used to control the generation of chaotic sequences, which makes the encryption algorithm highly relevant to the content of the image. Then, the hash value is embedded into the intermediate image according to the idea of steganography. In the second round of encryption, the image is encrypted under the control of another set of chaotic sequences to hide the hash value and further enhance the security of the algorithm. Different from other algorithms, our algorithm does not need to additionally transmit the hash value to the decryptor through a special channel. It has good availability and adaptability. Experimental results and security analysis demonstrate that the algorithm has high security performance and can resist various attacks. [ABSTRACT FROM AUTHOR]

How to choose a chaotic sequence to construct a chaotic S-box is a key factor to determine the performance of the S-box. In this paper, a construction method for chaotic S-box based on fireworks algorithm is proposed, in which the fireworks algorithm is used to search for the optimal solution in the solution space of the Lorenz chaotic system. The performances of S-box are tested through the nonlinearity, differential uniformity, strict avalanche criterion, output bits independence criterion and bijectivity, and compared with the existing classical S-boxes based on the Lorenz chaotic system. The results indicate that the S-box in this paper has more excellent cryptographic characteristics, which will provide a new idea for the efficient generation of chaotic S-box. [ABSTRACT FROM AUTHOR]

As image is an important way of information representation, researchers pay more and more attention on image encryption. In order to improve the performance of image encryption, a novel image encryption scheme based on a hybrid cascaded chaotic system and sectoral segmentation is proposed in this paper. Hybrid cascaded chaotic system has a larger key space, higher complexity, more sensitivity to initial conditions. Four chaotic sequences relevant to a plain image are generated by this system, which strengthen plaintext correlation and the randomness. During the scrambling process, sectoral segmentation focuses on how to extract a sequence from the disk storing data, which can not only reduce the correlation between the three components of the image, but also hide image information to a large extent. Further, a DNA algorithm is used in the diffusion process. Simulation shows that the proposed scheme can effectively resist various attacks and improve the encryption performance. [ABSTRACT FROM AUTHOR]

In this paper, an image encryption algorithm based on compressive sensing (CS) and a hyperchaotic system is proposed. This new two-dimensional logical coupling sine chaotic map (2D-LCSCM) has a wider range of chaos, better ergodicity and hyperchaotic properties rather than for existing chaotic maps. By combining with the novel chaotic map and CS, we design an image compression encryption algorithm with good reconstruction accuracy and high security. In the substitution phase of the encryption process, the security performance of the algorithm is improved by the nonlinear transformation of the dynamic substitution box (S-box) and the linear transformation of the chaotic sequences. The performance analyses of the experimental results show that the proposed algorithm can resist various attacks and is highly secure. [ABSTRACT FROM AUTHOR]

In this paper, a new spatiotemporal chaotic Parameter Uncertainty Mixed Coupled Map Lattice (PUMCML) is proposed. The Cantor diagonal matrix is generated from the Cantor set, and the ordered rotation scrambling strategy for this matrix is used to generate the scrambled image. Cantor set is a fractal system, so the Cantor set has a good effect on chaotic image encryption. The dynamic behavior of the PUMCML system is analyzed. The system has good chaotic property, so it is very suitable for chaotic image encryption. Using the PUMCML system, a diffusion strategy based on the mixture of Arnold and Logistic is proposed. Compared with other algorithms, the encryption effect of the proposed method is better and more secure. [ABSTRACT FROM AUTHOR]

The security of chaotic cryptographic system can be theoretically evaluated by using conventional statistical tests and numerical simulations, such as the character frequency test, entropy test, avalanche test and SP 800-22 tests. However, when the cryptographic algorithm operates on a cryptosystem, the leakage information such as power dissipation, electromagnetic emission and time-consuming can be used by attackers to analyze the secret keys, namely the Side Channel Analysis (SCA) attack. In this paper, a cryptanalysis method is proposed for evaluating the security of a chaotic block cryptographic system from a hardware perspective by utilizing the Template Attacks (TAs). Firstly, a chaotic block cryptographic system is described briefly and implemented based on an Atmel XMEGA microcontroller. Then the TA using a multivariate Gaussian model is introduced. In order to reduce computational complexity and improve the efficiency of TA, the Hamming weight is used in this work to model power consumption traces. The proposed TA method has the following advantages including (a) using the sum of difference to select points of interest of traces, (b) using a data processing method to minimize the influences on power information modeling from the redundant sampling points, and (c) all the traces are aligned precisely before establishing the templates. Experimental results show that the TA can be used to attack the chaotic cryptographic systems and is more efficient, i.e. ∼ 32% less attack traces than correlation power analysis, when the templates are properly built. [ABSTRACT FROM AUTHOR]

This paper introduces a new chaotic system model that could generate multi-direction multi-scroll (MDMS) chaotic attractors. The fundamental dynamics characteristics of this model are investigated, and the feasibility of the proposed method is confirmed by numerical simulation based on MATLAB. Additionally, the new chaotic system is implemented in FPGA-based platform. Implementation results are the same in MATLAB and FPGA, which indicates that they are suitable for practical applications. To investigate the cryptographic application of the new chaotic system, the chaotic sequences generated by the proposed system are used to encrypt images. The key space of the algorithm as well as key sensitivity, plain image sensitivity, plaintext histogram, correlation and information entropy are simulated and analyzed. In contrast to several encryption schemes, the proposed algorithm is very sensitive to plaintext and the key. [ABSTRACT FROM AUTHOR]

This paper is mainly devoted to the investigation of discrete-time fractional systems in three aspects. Firstly, the fractional Bogdanov map with memory effect in Riemann–Liouville sense is obtained. Then, via constructing suitable controllers, the fractional Bogdanov map is shown to undergo a transition from regular state to chaotic one. Meanwhile, the positive largest Lyapunov exponent is calculated by the Jacobian matrix algorithm to distinguish the chaotic areas. Finally, the Grassberger–Procaccia algorithm is employed to evaluate the correlation dimension of the controlled fractional Bogdanov system under different parameters. The main results show that the correlation dimension converges to a fixed value as the embedding dimension increases for the controlled fractional Bogdanov map in chaotic state, which also coincides with the conclusion driven by the largest Lyapunov exponent. Moreover, three-dimensional fractional Stefanski map is considered to further verify the effectiveness and generality of the obtained results. [ABSTRACT FROM AUTHOR]

To improve the robustness and imperceptibility of the existing coverless image information hiding, a generative coverless image information hiding algorithm based on fractal theory is proposed in this paper. Firstly, four fractal image generation methods are analyzed, and the relationship between the coverless information hiding and these methods is discussed. Secondly, based on the fractal image generation algorithm, secret information is hidden by controlling pixel rendering during the generation process. The robustness, imperceptibility, and capability of resisting steganalysis are balanced by adjusting the rendering distance. As it directly generates stego images, this can resist the detection of most existing steganalysis methods. Meanwhile, different capacities can be achieved by adjusting the size of the generated image. Experimental results and analysis show that the proposed scheme can effectively resist steganalysis and has good robustness against various image attacks. Furthermore, it can achieve large capacity, and it has broad prospects for covert communication. [ABSTRACT FROM AUTHOR]

In this paper, we propose an image encryption algorithm based on random walk and two hyperchaotic systems. The random walk method is adopted to scramble the position of pixels within a block. Furthermore, the permutation operation between blocks is presented to enhance the scramble effect. Thus, high correlation among pixels of original image is broken by permutation. Moreover, the chosen plaintext attack is used to test the anti-attack ability of the proposed algorithm. By analyzing experimental results and comparing with other image encryption algorithms, we show that the proposed algorithm has better performance and higher security. [ABSTRACT FROM AUTHOR]

A codimension-three Takens–Bogdanov bifurcation in reversible systems has been very recently analyzed in the literature. In this paper, we study with the help of the nonlinear time transformation method, the codimension-one and -two homoclinic and heteroclinic connections present in the corresponding unfolding. The algorithm developed allows to obtain high-order approximations for the global connections, in such a way that it supplies in a very efficient manner the coefficients that would be obtained with high-order Melnikov functions. As we show, all our analytical predictions have excellent agreement with the numerical results. In particular we remark that, for the two different codimension-two points, the theoretical approximation coincides in six decimal digits with the numerical continuation, even being quite far from the codimension-three point. The better approximations we provide in this work will help in the study of reversible systems that exhibit this codimension-three Takens–Bogdanov bifurcation. [ABSTRACT FROM AUTHOR]

In recent years, scholars studied and proposed some secure color image encryption algorithms. However, the majority of the published algorithms encrypted red, green and blue (called R , G , B for short) components independently. In the paper, we propose a color image encryption scheme based on hyperchaotic system and permutation-diffusion architecture. The encryption algorithm utilizes a block permutation which is realized by mixing R , G , B components to strengthen the dependence of each component. Besides, it can reduce time consumption. Then, the key streams generated by the hyperchaotic system are exploited to diffuse the pixels, the three components affect each other again. And in the diffusion process, we can get two totally different encrypted images even though we change the last pixel because the G component is diffused in reverse order. The experimental results reveal that our algorithm possesses better abilities of resisting statistical attacks and differential attacks, larger key space, closer information entropy to 8, and faster encryption speed compared with other chaos-based color image encryption algorithms. [ABSTRACT FROM AUTHOR]

At present, the performance of the digital chaotic sequence generator is affected by the calculation precision of processor and quantization method, which leads to the quantized chaotic binary sequences emerging from some periodic phenomena in the local range of sequences. However, in view of the current methods for analyzing the periodicity and randomness of binary sequences, evaluating the periodic characteristics which exist in the local range of chaotic binary sequences is extremely difficult. Therefore, in this paper, we have proposed a novel algorithm called the GBSPD (General Binary Sequences Periodic Detection) algorithm, which can detect typical periodic phenomena and local periodic phenomena in the chaotic binary sequence. Moreover, it can accurately locate the position of periodic phenomena of binary sequences and perform a detailed statistical analysis. Furthermore, by using the GBSPD algorithm to detect the periodic characteristics of the quantified logistic chaotic binary sequences, the experimental results show that the algorithm can effectively locate multiple periodic phenomena in the binary sequences. [ABSTRACT FROM AUTHOR]

At present, the performance of the digital chaotic sequence generator is affected by the calculation precision of processor and quantization method, which leads to the quantized chaotic binary sequences emerging from some periodic phenomena in the local range of sequences. However, in view of the current methods for analyzing the periodicity and randomness of binary sequences, evaluating the periodic characteristics which exist in the local range of chaotic binary sequences is extremely difficult. Therefore, in this paper, we have proposed a novel algorithm called the GBSPD (General Binary Sequences Periodic Detection) algorithm, which can detect typical periodic phenomena and local periodic phenomena in the chaotic binary sequence. Moreover, it can accurately locate the position of periodic phenomena of binary sequences and perform a detailed statistical analysis. Furthermore, by using the GBSPD algorithm to detect the periodic characteristics of the quantified logistic chaotic binary sequences, the experimental results show that the algorithm can effectively locate multiple periodic phenomena in the binary sequences. [ABSTRACT FROM AUTHOR]

The paper discusses the fractional Rössler system and the dependence of its dynamics on some entry parameters. An explicit algorithm for a priori determination of fractional Hopf bifurcations is derived and scenarios documenting a route of the system from stability to chaos are performed with respect to a varying system’s fractional order as well as to a varying system’s coefficient. Contrary to the existing results, the searched values of the fractional Hopf bifurcations follow directly from a revealed analytical dependence between these two systems’ entries. Their various critical values are established and confirmed by numerical experiments demonstrating not only the loss of stability of an equilibrium point, but also other phenomena of transition to chaotic behavior. In addition, we suggest an active control method for synchronization of two chaotic fractional-order Rössler systems. Our theoretical analysis enables to synchronize them for any value of a free parameter under which the master system displays a chaotic behavior. [ABSTRACT FROM AUTHOR]

The increasing need for image communication and storage has created a great necessity for securely transforming and storing images over a network. Whereas traditional image encryption algorithms usually consider the security of the whole plain image, region of interest (ROI) encryption schemes, which are of great importance in practical applications, protect the privacy regions of plain images. Existing ROI encryption schemes usually adopt approximate techniques to detect the privacy region and measure the quality of encrypted images; however, their performance is usually inconsistent with a human visual system (HVS) and is sensitive to statistical attacks. In this paper, we propose a novel privacy-aware ROI image encryption (PRIE) scheme based on logistical mapping and data hiding. The proposed scheme utilizes salient object detection to automatically, adaptively and accurately detect the privacy region of a given plain image. After private pixels have been encrypted using chaotic cryptography, the significant bits are embedded into the nonprivacy region of the plain image using data hiding. Extensive experiments are conducted to illustrate the consistency between our automatic ROI detection and HVS. Our experimental results also demonstrate that the proposed scheme exhibits satisfactory security performance. [ABSTRACT FROM AUTHOR]

This paper presents a study of two-dimensional hexagonal cellular automata (CA) with periodic boundary. Although the basic construction of a cellular automaton is a discrete model, its global level behavior at large times and on large spatial scales can be a close approximation to a continuous system. Meanwhile CA is a model of dynamical phenomena that focuses on the local behavior which depends on the neighboring cells in order to express their global behavior. The mathematical structure of the model suggests the importance of the algebraic structure of cellular automata. After modeling the dynamical behaviors, it is sometimes an important problem to be able to move backwards on CAs in order to understand the behaviors better. This is only possible if cellular automaton is a reversible one. In the present paper, we study two-dimensional finite CA defined by hexagonal local rule with periodic boundary over the field ℤ3 (i.e. 3-state). We construct the rule matrix corresponding to the hexagonal periodic cellular automata. For some given coefficients and the number of columns of hexagonal information matrix, we prove that the hexagonal periodic cellular automata are reversible. Moreover, we present general algorithms to determine the reversibility of 2D 3-state cellular automata with periodic boundary. A well known fact is that the determination of the reversibility of a two-dimensional CA is a very difficult problem, in general. In this study, the reversibility problem of two-dimensional hexagonal periodic CA is resolved completely. Since CA are sufficiently simple to allow detailed mathematical analysis, also sufficiently complex to produce chaos in dynamical systems, we believe that our construction will be applied many areas related to these CA using any other transition rules. [ABSTRACT FROM AUTHOR]

The aim of this paper is to compute the topological entropy of the real cubic polynomials , where , in certain cases. To accomplish this, some algorithms for counting the number of laps of , the th iteration of , are presented. [ABSTRACT FROM AUTHOR]

This paper compares the performance of Differential Evolution (DE) with Self-Organizing Migrating Algorithm (SOMA) in the task of optimization of the control of chaos. The main aim of this paper is to show that evolutionary algorithms like DE are capable of optimizing chaos control, leading to satisfactory results, and to show that extreme sensitivity of the chaotic environment influences the quality of results on the selected EA, construction of cost function (CF) and any small change in the CF design. As a model of deterministic chaotic system, the two-dimensional Henon map is used and two complex targeting cost functions are tested. The evolutionary algorithms, DE and SOMA were applied with different strategies. For each strategy, repeated simulations demonstrate the robustness of the used method and constructed CF. Finally, the obtained results are compared with previous research. [ABSTRACT FROM AUTHOR]

Chaotic Ant Swarm (CAS) is an optimization algorithm based on swarm intelligence theory, which has been applied to find the global optimum solution in search space. However, it often loses its effectiveness and advantages when applied to large and complex problems, e.g. those with high dimensions. To resolve the problems of high computational complexity and low solution accuracy existing in CAS, we propose a Disturbance Chaotic Ant Swarm (DCAS) algorithm to significantly improve the performance of the original algorithm. The aim of this paper is achieved by three strategies which include modifying the method of updating ant's best position, neighbor selection method and establishing a self-adaptive disturbance strategy. The global convergence of the DCAS algorithm is proved in this paper. Extensive computational simulations and comparisons are carried out to validate the performance of the DCAS on two sets of benchmark functions with up to 1000 dimensions. The results show clearly that DCAS substantially enhances the performance of the CAS paradigm in terms of computational complexity, global optimality, solution accuracy and algorithm reliability for complex high-dimensional optimization problems. [ABSTRACT FROM AUTHOR]

In this paper we discuss two modifications of the surrogate data method based on phase randomization, see [Theiler et al., 1992]. By construction, phase randomized surrogates are circular stationary. In this respect they differ from the original time series. This can cause level inaccuracies of surrogate data tests. We will illustrate this. These inaccuracies are caused by end to end mismatches of the original time series. In this paper we will discuss two approaches to remedy this problem: resampling from subsequences without end to end mismatches and data tapering. Both methods can be understood as attempts to make non-circular data approximately circular. We will show that the first method works quite well for a large range of applications whereas data tapering leads only to improvements in some examples but can be very unstable otherwise. [ABSTRACT FROM AUTHOR]

This paper presents an approach to control the chaotic dynamics of discrete-time (or discretizable) systems. The objective of the paper is to focus on the suppression of the chaotic dynamics and the restoration of order with a state feedback controller. The proposed control method works by targeting instantaneous measures of the Lyapunov exponents of a system and setting them to desired values. At first, the paper presents an instantaneous measure of the Lyapunov exponents; this measure is used to control the system's dynamics. Then, the formulation of the control algorithm to suppress chaos is presented. Two cases for the control structure are considered. The first case corresponds to the case when the number of control inputs is equal to the number of states; the second case corresponds to the case when the number of control inputs is less than the number of states. The Lorenz system, the smooth Chua Oscillator system, the Rössler-hyperchaos system and a fourth order chaotic oscillator system are used as examples to illustrate the proposed control scheme. The simulation results show the efficacy of the proposed control approach. [ABSTRACT FROM AUTHOR]

In this paper, we carefully reexamine the chaotic RF model, first studied by Rabinovich and Fabrikant [1979], and have found many new and rich complex dynamics of the model that were mostly not reported before. The chaotic RF model has proved to be a great challenge to classical numerical methods, in the sense that most classical numerical methods have not been very successful in the study of complex dynamics of this special RF model. Therefore, in this paper, we present and apply a special numerical method, the Local Iterative Linearization (LIL) method, along with a special Turbo Pascal code based on this accurate LIL algorithm, for a careful numerical study of this complex RF model. Many interesting new findings are summarized and reported in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the effect of the parameter switching (PS) algorithm in a fractional order chaotic circuit is investigated both in simulation and experiment. The Chen system of fractional order is focused and realized in an electronic circuit. By designing a switching circuit, the PS algorithm is implemented and it is the first time, the paradoxical 'Chaos Chaos Order' is presented in an electronic circuit. Both the simulation and experimental results confirm that the obtained attractor under switching approximates the attractor of the time-averaged model. Some important design issues for the circuitry realization of the PS scheme are pointed out. Finally, our work confirms the practical usage of PS algorithm in potential applications such as attractor synthesis and chaos control. [ABSTRACT FROM AUTHOR]

In this paper, we propose a dual particle swarm optimization (PSO) algorithm for parameter identification of chaotic systems. We also consider altering the search range of individual particles adaptively according to their objective function value. We consider both noiseless and noisy channels between the original system and the estimation system. Finally, we verify the effectiveness of the proposed dual PSO method by estimating the parameters of the Lorenz system using two different data acquisition schemes. Simulation results show that the proposed method always outperforms the traditional PSO algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a novel discrete differential evolution (DDE) algorithm is proposed to solve the vehicle routing problems (VRP) in B2C e-commerce, in which VRP is modeled by the incomplete graph based on the actual urban road system. First, a variant of classical VRP is described and a mathematical programming model for the variant is given. Second, the DDE is presented, where individuals are represented as the sequential encoding scheme, and a novel reparation operator is employed to repair the infeasible solutions. Furthermore, a FLOYD operator for dealing with the shortest route is embedded in the proposed DDE. Finally, an extensive computational study is carried out in comparison with the predatory search algorithm and genetic algorithm, and the results show that the proposed DDE is an effective algorithm for VRP in B2C e-commerce. [ABSTRACT FROM AUTHOR]

This paper introduces the capacitated vehicle routing problem with recycling in reverse logistics, and designs a food chain algorithm for it. Some illustrative examples are selected to conduct simulation and comparison. Numerical results show that the performance of the food chain algorithm is better than the genetic algorithm, particle swarm optimization as well as quantum evolutionary algorithm. [ABSTRACT FROM AUTHOR]

Ontology, a model of knowledge representation and storage, has had extensive applications in pharmaceutics, social science, chemistry and biology. In the age of 'big data', the constructed concepts are often represented as higher-dimensional data by scholars, and thus the sparse learning techniques are introduced into ontology algorithms. In this paper, based on the alternating direction augmented Lagrangian method, we present an ontology optimization algorithm for ontological sparse vector learning, and a fast version of such ontology technologies. The optimal sparse vector is obtained by an iterative procedure, and the ontology function is then obtained from the sparse vector. Four simulation experiments show that our ontological sparse vector learning model has a higher precision ratio on plant ontology, humanoid robotics ontology, biology ontology and physics education ontology data for similarity measuring and ontology mapping applications. [ABSTRACT FROM AUTHOR]

We propose a new primal-dual interior-point predictor-corrector algorithm in Ai and Zhang's wide neighborhood for solving monotone linear complementarity problems (LCP). Based on the understanding of this neighborhood, we use two new directions in the predictor step and in the corrector step, respectively. Especially, the use of new corrector direction also reduces the duality gap in the corrector step, which has good effects on the algorithm's convergence. We prove that the new algorithm has a polynomial complexity of , which is the best complexity result so far. In the paper, we also prove a key result for searching for the best step size along some direction. Considering local convergence, we revise the algorithm to be a variant, which enjoys both complexity of and Q-quadratical convergence. Finally, numerical result shows the effectiveness and superiority of the two new algorithms for monotone LCPs. [ABSTRACT FROM AUTHOR]

In this paper, the effect of delay on a nonlinear chaotic chemostat system with delayed feedback is investigated by regarding delay as a parameter. At first, the stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. Then an explicit algorithm for determining the direction and the stability of the bifurcating periodic solutions is derived by using the normal form theory and center manifold argument. Finally, some numerical simulation examples are given, which indicate that the chaotic oscillation can be converted into a stable steady state or a stable periodic orbit when delay passes through certain critical values. [ABSTRACT FROM AUTHOR]

In this paper, a general autonomous van der Pol-Duffing oscillator is studied. Several issues, such as periodic bifurcations and the dynamical structures of the system are investigated either analytically or numerically. Especially, a phenomenon of hidden attractors is noticed and an algorithm for the location of hidden attractors is given. The obtained results show that hidden attractors exist around chaotic attractors. [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of the correlation dimension estimated using the Grassberger-Procaccia (GP) algorithm [Grassberger & Procaccia, 1983] in the wavelet domain for functions belonging to Holder space. We prove that, as the wavelet scale level tends to infin-ity, the GP correlation dimension estimate tends to zero. Applying this result to the trajectories of the fractional Brownian motion process and using basic properties of the wavelet transform, we show that, for the fractional Gaussian noise process (fGn), the correlation dimension esti-mated by the GP procedure converges to the zero value. As the fractional Gaussian noise is a stochastic process with 1 /fα spectrum, --1 < α < 1, our results confirm Osborne and Proven-zale's assertion that colored random noise leads to the convergence of the GP-based correlation dimension estimator. However, our result holds for a different range of the spectrum exponent values. Moreover, for the fGn class of random processes, we found no correspondence between the value of the scaling exponent H and the value of the correlation dimension estimated by the GP algorithm as the latter is simply zero. [ABSTRACT FROM AUTHOR]

In this paper, the theory of regular chains and a triangular decomposition method relying on modular computations are presented in order to symbolically solve multivariate polynomial systems. Based on the focus values for dynamic systems obtained by using normal form theory, this method is applied to compute the limit cycles bifurcating from Hopf critical points. In particular, a quadratic planar polynomial system is used to demonstrate the solving process and to show how to obtain center conditions. The modular computations based on regular chains are applied to a cubic planar polynomial system to show the computation efficiency of this method, and to obtain all real solutions of nine limit cycles around a singular point. To the authors' best knowledge, this is the first article to simultaneously provide a complete, rigorous proof for the existence of nine limit cycles in a cubic system and all real solutions for these limit cycles. [ABSTRACT FROM AUTHOR]

This paper proposes to use a state feedback method to control the Hopf bifurcation for a novel congestion control model, i.e. the exponential random early detection (RED) algorithm with a single link and a single source. The gain parameter of the congestion control model is chosen as the bifurcation parameter. The analysis shows that in the absence of the state feedback controller, the model loses stability via the Hopf bifurcation early, and can maintain a stationary sending rate only in a certain domain of the gain parameter. When applying the state feedback controller to the model, the onset of the undesirable Hopf bifurcation is postponed. Thus, the stability domain is extended, and the model possesses a stable sending rate in a larger parameter range. Furthermore, explicit formulae to determine the properties of the Hopf bifurcation are obtained. Numerical simulations are given to justify the validity of the state feedback controller in bifurcation control. [ABSTRACT FROM AUTHOR]