Showing papers on "Chaotic published in 2012"

A chaotic circuit based on Hewlett-Packard memristor.

Abstract: Memristors are gaining increasing attention as next generation electronic devices. They are also becoming commonly used as fundamental blocks for building chaotic circuits, although often arbitrary (typically piece-wise linear or cubic) flux-charge characteristics are assumed. In this paper, a chaotic circuit based on the mathematical realistic model of the HP memristor is introduced. The circuit makes use of two HP memristors in antiparallel. Numerical results showing some of the chaotic attractors generated by this circuit and the behavior with respect to changes in its component values are described.

Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique

Abstract: In this paper, a novel fractional-order terminal sliding mode control approach is introduced to control/synchronize chaos of fractional-order nonautonomous chaotic/hyperchaotic systems in a given finite time. The effects of model uncertainties and external disturbances are fully taken into account. First, a novel fractional nonsingular terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then an appropriate robust fractional sliding mode control law is proposed to ensure the occurrence of the sliding motion in a given finite time. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. The proposed control scheme is applied to control/synchronize chaos of autonomous/nonautonomous fractional-order chaotic/hyperchaotic systems in the presence of both model uncertainties and external disturbances. Two illustrative examples are presented to show the efficiency and applicability of the proposed finite-time control strategy. It is worth to notice that the proposed fractional nonsingular terminal sliding mode control approach can be applied to control a broad range of nonlinear autonomous/nonautonomous fractional-order dynamical systems in finite time.

Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach

Abstract: In this paper we introduce a multiscale symbolic information-theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems. More precisely, we show that the multiscale complexity-entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system's dynamics. Numerical simulations obtained from the well-known and widely used Mackey-Glass oscillator operating in a high-dimensional chaotic regime were used as test beds. The effect of an increased amount of observational white noise was carefully examined. The results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles. Finally, several experimental and natural time series were analyzed in order to show the applicability of this scale-dependent symbolic approach in practical situations.

Image encryption algorithm using chaotic Chebyshev generator

Abstract: In this paper, we present a chaotic image encryption algorithm in which the key stream is generated by nonlinear Chebyshev function. The novel method of designing pseudorandom chaotic sequence is carried out with the created secret keys depending on with each other. We then make multiple permutation of pixels to decrease the strong correlation between adjacent pixels in original plain image. Further, a two-dimensional Chebyshev function is considered to avoid known-plaintext and chosen-plaintext attacks in diffusion process, i.e., even with a one-bit change in original plain image, the encrypted image would become different greatly. Simulation results are given to show that the proposed method can offer us an efficient way of encrypting image.

Transition from spatial coherence to incoherence in coupled chaotic systems.

Abstract: We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we find characteristic spatial patterns such as wavelike profiles and study the transition from coherence to incoherence leading to spatial chaos. We analyze the origin of this transition based on numerical simulations and support the results by theoretical derivations, identifying a critical coupling strength and a scaling relation of the coherent profiles. To demonstrate the universality of our findings, we consider time-discrete as well as time-continuous chaotic models realized as a logistic map and a R\"ossler or Lorenz system, respectively. Thereby, we establish the coherence-incoherence transition in networks of coupled identical oscillators.

A hybrid genetic algorithm and chaotic function model for image encryption

Abstract: The security of digital images has attracted much attention recently. In this study, a new method based on a hybrid model is proposed for image encryption. The hybrid model is composed of a genetic algorithm and a chaotic function. In the first stage of the proposed method, a number of encrypted images are constructed using the original image and the chaotic function. In the next stage, these encrypted images are used as the initial population for the genetic algorithm. In each stage of the genetic algorithm, the answer obtained from the previous iteration is optimized to produce the best-encrypted image. The best-encrypted image is defined as the image with the highest entropy and the lowest correlation coefficient among adjacent pixels. The use of genetic algorithms in image encryption has been attempted for the first time in this paper. Analyzing the results from the performed experiments, a high level of resistance of the proposed method against brute-force and statistical invasions is obviously illustrated. The obtained entropy and correlation coefficients of the method are approximately 7.9978 and −0.0009, respectively.

An efficient chaotic image encryption algorithm based on a generalized Arnold map

Abstract: An efficient image encryption algorithm using the generalized Arnold map is proposed. The algorithm is composed of two stages, i.e., permutation and diffusion. First, a total circular function, rather than the traditional periodic position permutation, is used in the permutation stage. It can substantially reduce the correlation between adjacent pixels. Then, in the stage of diffusion, double diffusion functions, i.e., positive and opposite module, are utilized with a novel generation of the keystream. As the keystream depends on the processed image, the proposed method can resist known- and chosen-plaintext attacks. Experimental results and theoretical analysis indicate the effectiveness of our method. An extension of the proposed algorithm to other chaotic systems is also discussed.

Explosive First-Order Transition to Synchrony in Networked Chaotic Oscillators

Abstract: Critical phenomena in complex networks, and the emergence of dynamical abrupt transitions in the macroscopic state of the system are currently a subject of the outmost interest We report evidence of an explosive phase synchronization in networks of chaotic units Namely, by means of both extensive simulations of networks made up of chaotic units, and validation with an experiment of electronic circuits in a star configuration, we demonstrate the existence of a first-order transition towards synchronization of the phases of the networked units Our findings constitute the first prove of this kind of synchronization in practice, thus opening the path to its use in real-world applications

Perception and self-organized instability.

Abstract: This paper considers state-dependent dynamics that mediate perception in the brain. In particular, it considers the formal basis of self-organized instabilities that enable perceptual transitions during Bayes-optimal perception. The basic phenomena we consider are perceptual transitions that lead to conscious ignition (Dehaene and Changeux, 2011) and how they depend on dynamical instabilities that underlie chaotic itinerancy (Breakspear, 2001; Tsuda, 2001) and self-organized criticality (Beggs and Plenz, 2003; Plenz and Thiagarajan, 2007; Shew et al., 2011). Our approach is based on a dynamical formulation of perception as approximate Bayesian inference, in terms of variational free energy minimization. This formulation suggests that perception has an inherent tendency to induce dynamical instabilities (critical slowing) that enable the brain to respond sensitively to sensory perturbations. We briefly review the dynamics of perception, in terms of generalized Bayesian filtering and free energy minimization, present a formal conjecture about self-organized instability and then test this conjecture, using neuronal (numerical) simulations of perceptual categorization.

Synchronization of fractional order chaotic systems using active control method

Abstract: In this article, the active control method is used for synchronization of two different pairs of fractional order systems with Lotka–Volterra chaotic system as the master system and the other two fractional order chaotic systems, viz., Newton–Leipnik and Lorenz systems as slave systems separately. The fractional derivative is described in Caputo sense. Numerical simulation results which are carried out using Adams–Bashforth–Moulton method show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order chaotic systems while it also allows both the systems to remain in chaotic states. A salient feature of this analysis is the revelation that the time for synchronization increases when the system-pair approaches the integer order from fractional order for Lotka–Volterra and Newton–Leipnik systems while it reduces for the other concerned pair.

A directed weighted complex network for characterizing chaotic dynamics from time series

Abstract: We propose a reliable method for constructing a directed weighted complex network (DWCN) from a time series Through investigating the DWCN for various time series, we find that time series with different dynamics exhibit distinct topological properties We indicate this topological distinction results from the hierarchy of unstable periodic orbits embedded in the chaotic attractor Furthermore, we associate different aspects of dynamics with the topological indices of the DWCN, and illustrate how the DWCN can be exploited to detect unstable periodic orbits of different periods Examples using time series from classical chaotic systems are provided to demonstrate the effectiveness of our approach

A hyperchaotic system without equilibrium

Abstract: This article introduces a new chaotic system of 4-D autonomous ordinary differential equations, which has no equilibrium. This system shows a hyper-chaotic attractor. There is no sink in this system as there is no equilibrium. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincare maps. There is little difference between this chaotic system and other chaotic systems with one or several equilibria shown by phase portraits, Lyapunov exponents and time series methods, but the Poincare maps show this system is a chaotic system with more complicated dynamics. Moreover, the circuit realization is also presented.

Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication

Abstract: This paper presents a new fractional-order hyperchaotic system. The chaotic behaviors of this system in phase portraits are analyzed by the fractional calculus theory and computer simulations. Numerical results have revealed that hyperchaos does exist in the new fractional-order four-dimensional system with order less than 4 and the lowest order to have hyperchaos in this system is 3.664. The existence of two positive Lyapunov exponents further verifies our results. Furthermore, a novel modified generalized projective synchronization (MGPS) for the fractional-order chaotic systems is proposed based on the stability theory of the fractional-order system, where the states of the drive and response systems are asymptotically synchronized up to a desired scaling matrix. The unpredictability of the scaling factors in projective synchronization can additionally enhance the security of communication. Thus MGPS of the new fractional-order hyperchaotic system is applied to secure communication. Computer simulations are done to verify the proposed methods and the numerical results show that the obtained theoretic results are feasible and efficient.

Modified projective synchronization of fractional-order chaotic systems via active sliding mode control

Abstract: This paper is devoted to study the problem of modified projective synchronization of fractional-order chaotic system. Base on the stability theorems of fractional-order linear system, active sliding mode controller is proposed to synchronize two different fractional-order systems. Moreover, the controller is robust to the bounded noise. Numerical simulations are provided to show the effectiveness of the analytical results.

Design of a High-Data-Rate Differential Chaos-Shift Keying System

Abstract: In a differential chaos-shift keying (DCSK) system, the reference and information chaotic bearing signals are transmitted in two consecutive time slots and require the presence of delay components in the modulator and demodulator circuits. This system design requires a difficult-to-implement radio-frequency delay line that limits the data rate. The code-shifted DCSK (CS-DCSK) system proposes a solution for these problems by spreading the two chaotic slots by Walsh codes instead of using a time delay and sending them during the same time interval. In this brief, we extend the study of the CS-DCSK system, and we design two versions of a high-data-rate CS-DCSK system, which increase the data rate and can also perform in a multiuser case. The idea to achieve a high data rate is to get the information bits to share the same reference chaotic slot, where their separation is assured and maintained by different chaotic signals. In addition, this new design is not limited to a restricted number of Walsh codes such as CS-DCSK and provides from the properties of the chaotic signal in terms of security and good correlation properties. Finally, the performances of the systems are analyzed.

A Chaotic Levy Flight Bat Algorithm for Parameter Estimation in Nonlinear Dynamic Biological Systems

Abstract: We propose a synergistic approach to meta-heuristic search optimization algorithm. The fine balance between intensification (exploitation) and diversification (exploration) is very important to the overall efficiency and performance of a meta-heuristic search algorithm. Too little exploration and too much exploitation could cause the system to be trapped in local optima, which makes it very difficult or even impossible to find the global optimum. The diversification via randomization provides a good way to move away from local search to the search on the global scale and avoids the solutions being trapped at local optima, while increases the diversity of the solutions. The good combination of these two major components will usually ensure that the global optimality is achievable. It is worth pointing that the use of a uniform distribution is not the only way to achieve randomization. In fact, random walks such as Levy flights on a global scale are more efficient. The track of chaotic variable can travel ergodically over the whole search space. In general, the chaotic variable has special characters, i.e., ergodicity, pseudo-randomness and irregularity. To enrich the searching behavior and to avoid being trapped into local optimum, chaotic sequence and a chaotic Levy flight are incorporated in the metaheuristic search for efficiently generating new solutions. We presented synergistic strategies for meta-heuristic optimization learning, with an emphasis on the balance between intensification and diversification. In this paper, we apply the proposed search optimization algorithm and describe a general methodology to adaptively select the values of the model parameters for the reconstruction of biological system dynamics. We illustrate the application of the method by jointly estimating the parameter vector of the dynamics of endocytosis.

An intertwining chaotic maps based image encryption scheme

Abstract: In this paper, a new image encryption scheme is proposed that uses intertwining chaotic maps to enhance security and key length. In the substitution process, six randomly chosen odd integers are used to permute and then XORed with the first chaotic key to shuffle and alter the image pixels. Byte substitution has also been applied and the resultant values are XORed with the second chaotic key to improve the security against the known/chosen-plain text attack and to increase nonlinearity. In the diffusion process, the pixel values are altered sequentially with various operations which include nonlinear diffusion using the first chaotic key, subdiagonal diffusion of adjacent pixels and XORing with the third chaotic key. The security and performance of the proposed image encryption technique have been analyzed using statistical analysis, sensitivity analysis, key space analysis, differential analysis, and entropy analysis. The simulation shows that a single bit of key or pixel difference of the plain-image will change almost all the pixels in the cipher-image ( $\mathrm{NPCR}>99.63$ %), and the unified average changing intensity is high ( $\mathrm{UACI}>33.43$ %). Since the entropy is found to be close to the theoretical value, we observed that the information leakage is negligible, and hence the scheme is highly secure. The experimental results show that the performance of the proposed scheme is secure and fast.

Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme

Abstract: This paper brings attention to the chaotic antisynchronization and synchronization for a novel class of chaotic systems with different structure and dimensions by using a new sliding mode control strategy. This approach needs only n−1 controllers, where n is the number of the salve system dimensions. And our method uses proportional integral (PI) surface and saturation function to simplify the task of assigning the performance of the closed-loop error system in sliding motion. Furthermore, the sufficient conditions are derived, and representative examples are proposed as well. Finally, numerical simulations are provided to verify the effectiveness and feasibility of the proposed control scheme, which are in agreement with theoretical analysis.