Control uncertain continuous－time chaotic dynamical system

The new chaos control method presented in this paper is useful for taking advantage of chaos.Based on sliding mode control theory, this paper provides a switching manifold controlling strategy of chaoticsystem, and also gives a kind of adaptive parameters estimated method to estimate the unknown systems' pa-rameters by which chaotic dynamical system can be synchronized. Taking the Lorenz system as example, and with the help of this controlling strategy, we can synchronize chaotic systems with unknown parameters and different initial conditions.

Generalized Synchronization in a Drive-Response System

The phenomena of GS in a drive-response system have been studied. Several kinds of GS are found： the driver-induced GS, the responser-induced GS, and the intermediate GS. The mechanism generating these types of GS is given and the roles played by response and drive dynamics in realizing different GS states are discussed.

Application of chaotic theory to parameter estimation

High precision parameter estimation is very important for control system design and compensation. This paper utilizes the properties of chaotic system for parameter estimation. Theoretical analysis and experimental results indicated that this method has extremely high sensitivity and resolving power. The most important contribution of this paper is apart from the traditional engineering viewpoint and actualizing parameter estimation just based on unstable chaotic systems.

Approach to Generalized Synchronization with Application to Chaos-Based Secure Communication

A constructive theorem is established for generalized synchronization (GS) related to C1 diffeomorphic transformations of unidirectionally coupled dynamical arrays. The theorem provides some interpretations about the underlying mechanism of various GS phenomena in nature. As a direct application of the theorem, a chaos-based secure Internet communication scheme is proposed. Moreover, a cellular neural network (CNN) of Chen's chaotic circuits with GS property is designed and studied. Numerical simulation shows that this Chen's CNN has high security and is fast and reliable for secure Internet communications.

Digital Communication Using Multi-mode Chaotic Lasers

The digital communication in a system of two multi-mode solid state chaotic lasers is investigated theoretically. If the usual method working well in a single-mode laser system is applied to a multi-mode laser system, the memory effect of the two nearest digits can cause high rate of mistakes when the digits are decoded through the subtraction of receiver output from the transmittal. By introducing the deviations of two nearest maximum and minimum fluctuationsof the signal to decode the digit, the message can be decoded correctly. Also, this communication method does not critically depend on the quality of the chaotic synchronization of the two multi-mode lasers.

Hyperchaos behaviors and chaos synchronization of two unidirectional coupled simplified Lorenz systems

To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.

Henon CSK Secure Communication System Using Chaotic Turbo Codes

In this paper, the authors design a novel chaotic secure communication system, which has high security and good error correcting capability. Firstly, the Henon Chaos Shift Keying (CSK) modulation block is presented. Secondly, chaotic turbo encoder/decoder (hard decision) is introduced. Thirdly, this chaotic secure communication system, which comprises the Henon CSK modulation block and chaotic turbo encoder in a serially concatenated form, is shown. Furthermore, a novel two step encryption scheme is proposed, which is based on the chaotic turbo encoded Henon CSK secure communication system.

On-Off Intermittency Route to Chaos Synchronization and Spatial Periodic Synchronization of Chaos in Coupled Arrays of Chaotic Systems

Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We find that chaos synchronization in circular arrays of chaotic systems can occur through the on off intermittent synchronization with a power law distribution of laminar phases. And in the coupled ring and linear array it is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the linear array.

An Image Encryption Approach Using a Shuffling Map

A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyvalues of the shuffled image according to the changed chaotic values of the same position between the above nonlinearchaotic sequence and the sorted chaotic sequence.The experimental results demonstrate that the image encryptionscheme based on a shuffling map shows advantages of large key space and high-level security.Compared with someencryption algorithms,the suggested encryption scheme is more secure.

AN H_∞ FUZZY TRACKING CONTROL SCHEME FOR AFFINE COUPLED SPATIO-TEMPORAL CHAOS

Due to the interactions among coupled spatio-temporal subsystems and the constant bias term of affine chaos, it is difficult to achieve tracking control for the affine coupled spatiotemporal chaos. However, every subsystem of the affine coupled spatio-temporal chaos can be approximated by a set of fuzzy models; every fuzzy model represents a linearized model of the subsystem corresponding to the operating point of the controlled system. Because the consequent parts of the fuzzy models have a constant bias term, it is very difficult to achieve tracking control for the affine system. Based on these fuzzy models, considering the affine constant bias term, an H∞ fuzzy tracking control scheme is proposed. A linear matrix inequality is employed to represent the feedback controller, and parameters of the controller are achieved by convex optimization techniques. The tracking control for the affine coupled spatio-temporal chaos is achieved, and the stability of the system is also guaranteed. The tracking performances are testified by simulation examples.

Synchronization of Spatiotemporal Chaos in Coupled Complex Ginzburg—Landau Oscillators

Synchronization of spatiotemporal distributed system is investigated by considering the model of 1D dif-fusively coupled complex Ginzburg-Landau oscillators. An itinerant approach is suggested to randomly move turbulentsignal injections in the space of spatiotemporal chaos. Our numerical simulations show that perfect turbulence synchro-nization can be achieved with properly selected itinerant time and coupling intensity.

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

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

Using chaos to improve measurement precision

If the measuring signals were input to the chaotic dynamic system as initial parameters, the system outputs might be in steady state, periodic state or chaos state. If the chaotic dynamic system outputs controlled in the periodic states, the periodic numbers would be changed most with the signals. Our novel method is to add chaotic dynamic vibration to the measurement or sensor system.The sensor sensitivity and precision of a measurement system would be improved with this method. Chaotic dynamics measurement algorithms are given and their sensitivity to parameters are analyzed in this paper. The effects of noises on the system are discussed.

A New Approach for Controlling Chaos Based on Direct Optimizing Predictive Control

We introduce the predictive control theory into predictive control algorithm based on a neural network model the study of chaos control and propose a direct optimizing The proposed control system stabilizes the chaotic motion in an unknown chaotic system onto the desired target trajectory. Compared with the existing similar algorithms, the proposed control system has faster response, so it requires much shorter time for the stabilization of the chaotic systems. The proposed approach can control hyperchaos and the algorithm is simple. The convergence of the control algorithm and the stability of the control system can be guaranteed. The theoretic analysis and simulations demonstrate the effectiveness of the algorithm.

Control of a Unified Chaotic System via Single Variable Feedback

Based on the LaSalle invariance principle, we propose a simple adaptive-feedback for controlling the unified chaotic system. We show explicitly with numerical proofs that our method can easily achieve the control of chaos in the unified chaotic system using only a single variable feedback. The present controller, to our knowledge, is the simplest control scheme for controlling a unified chaotic system.

Fractal Structures and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.

Research on Stream Cipher Model Based on Chaos Theory

Chaos is a similar and random process which is very sensitive to initial value in deterministic system. It is a performance of nonlinear dynamical system with built-in randomness. Combined with the advantages and disadvantages of the present chaos encryption model, the paper proposes a chaotic stream cipher model based on chaos theory, which not only overcomes finite precision effect, but also improves the randomness of chaotic system and output sequence. The Sequence cycle theory generated by the algorithm can reach more than 10600 at least, which completely satisfies the actual application requirements of stream cipher system.

Sensitivity of Coupled Chaotic Dynamical System to Parameters in the Context of Data Assimilation

In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biological and engineering sciences. A major component of this tool is a coupled chaotic dynamical system obtained by coupling two versions of the well-known Lorenz （1963） model with different time scales which differ by a certain time-scale factor. A tangent linear model and its adjoint are considered that correspond to a coupled chaotic system. The general idea of applying sensitivity measures （sensitivity functions） to coupled systems, emphasizing the data assimilation aspects, is explored as well by the forward sensitivity approach. For this purpose the set of sensitivity equations is derived from the nonlinear equations of the coupled dynamical system. To estimate the influence of model parameter uncertainties on the simulated state variables the relative error in the energy norm is used.

Synchronization of perturbed chaotic systems via nonlinear control

Chaos synchronization of systems with perturbations was investigated.A generic nonlinear control scheme to realize chaos synchronization of systems was proposed.This control scheme is flexible and practicable,and gives more freedom in designing controllers in order to achieve some desired performance.With the aid of Lyapunov stability theorem and partial stability theory,two cases were presented:1) Chaos synchronization of the system without perturbation or with vanishing perturbations;2) The boundness of the error state for the system with nonvanishing perturbations satisfying some conditions.Finally,several simulations for Lorenz system were provided to verify the effectiveness and feasibility of our method.Compared numerically with the existing results of linear feedback control scheme,the results are sharper than the existing ones.