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Abstract: In this paper, an adaptive algorithm is proposed for synchronization of chaotic systems with different orders. A modular adaptive control strategy is applied to make states of the slave system track those of the master, despite the unknown parameters. One of the most advantages of the modularity approach, which is applied for the first time in chaos synchronization, is its flexibility in choosing identification and control modules and designing them completely independently. In this paper, a modified recursive least square algorithm is used to identify the unknown parameters of the slave system, and the control module is designed by means of two different algorithms. First it is designed based on active control method, and then, in order to synchronize with a lower energy, we design an optimal controller. The two methods are applied on a practical case study, and the results are compared. Two different dimensional neuron models, the HR neuron model and the cable model of cylindrical cell, are considered as the master and slave systems, respectively. Simulation results confirm the effectiveness of the proposed method. [Copyright &y& Elsevier]

In this paper, the problem of chaos control in discrete-time chaotic systems with unknown governing equations and limited measurable states is investigated. Using the time-series of only one measurable state, an algorithm is proposed to stabilize unstable fixed points. The approach consists of three steps: first, using Takens embedding theory, a delayed phase space preserving the topological characteristics of the unknown system is reconstructed. Second, a dynamic model is identified by recursive least squares method to estimate the time-series data in the delayed phase space. Finally, based on the reconstructed model, an appropriate linear delayed feedback controller is obtained for stabilizing unstable fixed points of the system. Controller gains are computed using a systematic approach. The effectiveness of the proposed algorithm is examined by applying it to the generalized hyperchaotic Henon system, prey-predator population map, and the discrete-time Lorenz system. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a control method that generates a desired limit-cycle-like behavior for a 2-dimensional discrete-time nonlinear control system is discussed. First, we define some notations and state the problem formulation. Next, a necessary and sufficient condition of existence of a control input that realizes a desired limit-cycle-like behavior is shown. We then derive a control algorithm to solve the problem on generating limit-cycle-like behaviors, and a modification of the algorithm is also shown. Finally, we apply the two types of algorithms to a chaotic system, the Hénon map, in order to indicate the availability of the proposed method. In addition, by using the control method, we also consider a stabilization problem for the Hénon map. [Copyright &y& Elsevier]

Abstract: Many discrete-time dynamical systems have a region Q from which all or almost all trajectories leave, or at least they leave in the presence of perturbations that we call disturbances. We partially control systems so that despite disturbances the trajectories of a dynamical system stay in the region Q at least for some initial points in Q. The disturbances can be thought of as either noise or as purposeful, hostile efforts of an enemy to drive the trajectory out of the region. Our goal is to keep trajectories inside Q despite the disturbances and our partial control of chaos method succeeds. Surprisingly this goal can be achieved with a control whose maximum allowable size is smaller than the maximum allowed disturbance. A fundamental step towards this goal is to compute a set called the safe set that had, until now, been found only in certain very special situations. This paper provides a general algorithm for computing safe sets. The algorithm is able to compute the safe sets for a specified region in phase space, the maximum disturbance value, and the maximum allowed control. We call it the Sculpting Algorithm. Its operation is analogous to removing material while sculpting a statue. The algorithm sculpts the safe sets. Our Sculpting Algorithm is independent of the dimension and is fast for one- and two-dimensional dynamical systems. As examples, we apply the algorithm to two paradigmatic nonlinear dynamical systems, namely, the Hénon map and the Duffing oscillator. [Copyright &y& Elsevier]

Abstract: In this paper, we suggest a new steganographic spatial domain algorithm based on a single chaotic map. Unlike most existing steganographic algorithms, the proposed algorithm uses one chaotic map to determine the pixel position of the host color image, the channel (red, green or blue) and the bit position of the targeted value in which a sensitive information bit can be hidden. Furthermore, this algorithm can be regarded as a variable-sized embedding algorithm. Experimental results demonstrate that this algorithm can defeat many existing steganalytic attacks. In comparison with existing steganographic spatial domain based algorithms, the suggested algorithm is shown to have some advantages over existing ones, namely, larger key space and a higher level of security against some existing attacks. [Copyright &y& Elsevier]

Abstract: Recently [Solak E, Çokal C, Yildiz OT Biyikogˇlu T. Cryptanalysis of Fridrich’s chaotic image encryption. Int J Bifur Chaos 2010;20:1405–1413] cryptanalyzed the chaotic image encryption algorithm of [Fridrich J. Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifur Chaos 1998;8(6):1259–1284], which was considered a benchmark for measuring security of many image encryption algorithms. This attack can also be applied to other encryption algorithms that have a structure similar to Fridrich’s algorithm, such as that of [Chen G, Mao Y, Chui, C. A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Soliton Fract 2004;21:749–761]. In this paper, we suggest a novel image encryption algorithm based on a three dimensional (3D) chaotic map that can defeat the aforementioned attack among other existing attacks. The design of the proposed algorithm is simple and efficient, and based on three phases which provide the necessary properties for a secure image encryption algorithm including the confusion and diffusion properties. In phase I, the image pixels are shuffled according to a search rule based on the 3D chaotic map. In phases II and III, 3D chaotic maps are used to scramble shuffled pixels through mixing and masking rules, respectively. Simulation results show that the suggested algorithm satisfies the required performance tests such as high level security, large key space and acceptable encryption speed. These characteristics make it a suitable candidate for use in cryptographic applications. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a dedicated keyed hash algorithm based on the modified coupled chaotic map lattice. By using the nearest and long distance couplings, both the key and the message as the parameters of the coupled map lattice, the expansion key and the nonlinear transformation, the system has enough confusion and diffusion rate between the message and the key. The structure of the system provides strong collision resistance and high performance efficiency. Simulation results show that the system has a uniform and random distribution of hash value, and fast performance. [Copyright &y& Elsevier]

Abstract: In this paper, particle swarm optimization (PSO) is applied to synchronize chaotic systems in presence of parameter uncertainties and measurement noise. Particle swarm optimization is an evolutionary algorithm which is introduced by Kennedy and Eberhart. This algorithm is inspired by birds flocking. Optimization algorithms can be applied to control by defining an appropriate cost function that guarantees stability of system. In presence of environment noise and parameter uncertainty, robustness plays a crucial role in succeed of controller. Since PSO needs only rudimentary information about the system, it can be a suitable algorithm for this case. Simulation results confirm that the proposed controller can handle the uncertainty and environment noise without any extra information about them. A comparison with some earlier works is performed during simulations. [Copyright &y& Elsevier]

Abstract: The pseudo-randomness and complexity of binary sequences generated by chaotic systems are investigated in this paper. These chaotic binary sequences can have the same pseudo-randomness and complexity as the chaotic real sequences that are transformed into them by the use of Kohda’s quantification algorithm. The statistical test, correlation function, spectral analysis, Lempel–Ziv complexity and approximate entropy are regarded as quantitative measures to characterize the pseudo-randomness and complexity of these binary sequences. The experimental results show the finite binary sequences generated by the chaotic systems have good properties with the pseudo-randomness and complexity of sequences. However, the pseudo-randomness and complexity of sequence are not added with the increase of sequence length. On the contrary, they steadily decrease with the increase of sequence length in the criterion of approximate entropy and statistical test. The constraint of computational precision is a fundamental reason resulting in the problem. So only the shorter binary sequences generated by the chaotic systems are suitable for modern cryptography without other way of adding sequence complexity in the existing computer system. [Copyright &y& Elsevier]

Abstract: Recently, many scholars have proposed chaotic cryptosystems in order to promote communication security. However, there are a number of major problems detected in some of those schemes such as weakness against differential attack, slow performance speed, and unacceptable data expansion. In this paper, we introduce a new chaotic block cipher scheme for image cryptosystems that encrypts block of bits rather than block of pixels. It encrypts 256-bits of plainimage to 256-bits of cipherimage within eight 32-bit registers. The scheme employs the cryptographic primitive operations and a non-linear transformation function within encryption operation, and adopts round keys for encryption using a chaotic system. The new scheme is able to encrypt large size of images with superior performance speed than other schemes. The security analysis of the new scheme confirms a high security level and fairly uniform distribution. [Copyright &y& Elsevier]

Abstract: A block encryption for image using combination of confusion and diffusion is proposed in this paper. In this encryption, a new compound mode is proposed. Baker map is used to generate a pseudo-random sequence, and several one-dimension chaotic maps are dynamically selected to encrypt blocks of image, in the order of the pseudo-random sequence generated by Baker map. Different with other combined encryptions, the algorithm of this encryption does not confusion original image directly, but generate a pseudo-random, which is used as a route for diffusion, combines pixels to block randomly and arrays them. When diffusion is executing, for mutual diffusion of pixels, the confusion is working by the pseudo-random order of route, the combination is deep-seated. [Copyright &y& Elsevier]

Abstract: In this paper, a novel image encryption scheme using coupled map lattices (CML) with time delay is proposed. By employing discretized tent map to shuffle the positions of image pixels and then using delayed coupled map lattices (DCML) to confuse the relationship between the plain-image and the cipher-image, image encryption algorithms with permutation-diffusion structure are introduced in detail. In the process of generating keystream, the time-varying delay is also embedded in our proposed scheme to enhance the security. Theoretical analysis and computer experiments confirm that the new algorithm possesses high security for practical image encryption. [Copyright &y& Elsevier]

Abstract: Recently, a variety of chaos-based hash functions have been proposed. Nevertheless, none of them can realize modification localization. In this paper, a hash function with both modification detection and localization capabilities is proposed, which can also support the parallel processing mode. By using the mechanism of changeable-parameter and self-synchronization, the keystream can establish a close relation with the algorithm key, the content, and the order of each message unit. Theoretical analysis and computer simulation indicate that the proposed algorithm can satisfy the performance requirements of hash functions. [Copyright &y& Elsevier]

Abstract: In this paper, nonlinear time series modeling techniques are applied to analyze building energy consumption data. The time series were obtained for the benchmark data set Proben 1, and comes from the first energy prediction contest, the Great Building Energy Predictor Shootout I, organized by ASHRAE. The phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem suggested by TAKENS. The embedding parameters, e.g. the delay time and the embedding dimension are estimated using the average mutual information (AMI) of the data and the false nearest neighbor (FNN) algorithm, respectively. Nonlinearity was detected, by applying the surrogate data sets method. Numerically estimated non-integral fractal dimension and a positive Lyapunov exponent are not necessarily sufficient indication of chaos; therefore we apply a more stringent criterion, developed by Gao and Zheng, which is based on the logarithmic displacement of time-dependent exponent curves, and show that these data are chaotic. Based on this analysis and proof, we then calculate the correlation dimension of the resulting attractor and the largest Lyapunov exponent. The correlation dimension 3.47 and largest Lyapunov exponent 0.047 are estimated. These results indicate that chaotic characteristics obviously exist in the specific energy consumption data set, and thus techniques based on phase space dynamics can be used to analyze and predict buildings energy use. [Copyright &y& Elsevier]

Abstract: The construction of a new Hash function attracts much attention recently. In Kwok and Tang (2005) [Kwok HS, Tang WKS. A chaos-based cryptographic Hash function for message authentication. Int J Bifurcat Chaos 2005;15:4043–50], a chaos-based Hash function has been proposed. In this paper, the potential flaws in the original algorithm are analyzed in detail, and then the corresponding improving measures are proposed. We enhance the influence that each bit of the final Hash value is closely related to all the bits of the message or key and a single bit change in message or key results in great changes in the final Hash value. Simulation results show that the proposed improving algorithm has strong diffusion and confusion capability, good collision resistance, extreme sensitivity to message and secret key. [Copyright &y& Elsevier]

Abstract: This paper describes the security weakness of a recently proposed image encryption algorithm based on a logistic-like new chaotic map. We show that the chaotic map’s distribution is far from ideal, thus making it a bad candidate as a pseudo-random stream generator. As a consequence, the images encrypted with this algorithm are shown to be breakable through different attacks of variable complexity. [Copyright &y& Elsevier]

Abstract: Chaos is undesirable in many engineering applications since it causes a serious degradation of the system performance and restricts the system’s operating range. Therefore, the problem of controlling chaos has attracted intense interest in recent years. This paper proposes an approach for optimizing the control of chaotic systems with input saturation using an input-state linearization scheme. In the proposed approach, the optimal system gains are identified using the Nelder–Mead simplex algorithm. This algorithm does not require the derivatives of the cost function (or the performance index) to be optimized, and is therefore particularly applicable to problems with undifferentiable elements or discontinuities. Two numerical simulations are performed to demonstrate the feasibility and effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, a new reliable algorithm based on an adaptation of the standard homotopy analysis method (HAM) is presented, which is the multistage homotopy analysis method (MSHAM). The freedom of choosing the auxiliary linear operator and the auxiliary parameter are still present in the MSHAM. The solutions of the non-chaotic and the chaotic Chen system which is a three-dimensional system of ordinary differential equations with quadratic nonlinearities were obtained by MSHAM. Numerical comparisons between the MSHAM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for solving the non-linear chaotic and non-chaotic Chen system. [Copyright &y& Elsevier]

Abstract: In this paper, we consider chaos synchronization between chaotic Colpitts oscillators with different orders, consisting of standard and improved version of Colpitts oscillators. Firstly, the normalized state equation of the improved version of the Colpitts oscillator designed to operate in the ultrahigh frequency range are presented. It is found that this version is described by fourth-order nonlinear differential equations. The equations of motion are solved numerically using the Runge–Kutta algorithm and simulations demonstrate chaos in the microwave frequencies range. Secondly, the problem of synchronization dynamics of third and fourth orders systems in the chaotic states is also investigated, and a controller is proposed based on stability theory by constructing the Lyapunov function, to ensure synchronization between both oscillators. Computer experiments demonstrate the effectiveness and feasibility of the proposed technique for these oscillators. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to investigate the accuracy of the differential transformation method (DTM) for solving the hyperchaotic Rössler system, which is a four-dimensional system of ODEs with quadratic nonlinearities. Comparisons between the DTM solutions and the fourth-order Runge–Kutta (RK4) solutions are made. The DTM scheme obtained from the DTM yields an analytical solution in the form of a rapidly convergent series. The direct symbolic-numeric scheme is shown to be efficient and accurate. [Copyright &y& Elsevier]

Abstract: This paper proposes an approach for detecting unstable periodic orbits embedded in chaotic systems by using the simplex method. The simplex algorithm is easily implemented and does not require the derivatives of the function to be optimized. As a result, it is also applicable to chaotic systems with discontinuities or in which functions contain noise. [Copyright &y& Elsevier]

Abstract: A block encryption algorithm using dynamic sequences generated by multiple chaotic systems is proposed in this paper. In this algorithm, several one-dimension chaotic maps generate pseudo-random sequences, which are independent and approximately uniform. After a series of transformations, the sequences constitute a new pseudo-random sequence uniformly distributing in the value space, which covers the plaintext by executing Exclusive-OR and shifting operations some rounds to form the cipher. This algorithm makes the pseudo-random sequence possess more concealment and noise like characteristic, and overcomes the periodic malpractice caused by the computer precision and single chaotic system. Simulation results show that the algorithm is efficient and useable for the security of communication system. [Copyright &y& Elsevier]