Dimensional Chaotic Systems Research Articles

Synchronization New 3D Chaotic System Using Brain Emotional Learning Based Intelligent Controller

One of the most important phenomena of some systems is chaos which is caused by nonlinear dynamics. In this paper, the new 3 dimensional chaotic system is firstly investigated and then utilizing an intelligent controller which based on brain emotional learning (BELBIC), this new chaotic system is synchronized. The BELBIC consists of reward signal which accept positive values. Improper selection of the parameters causes an improper behavior which may cause serious problems such as instability of system. It is needed to optimize these parameters. Genetic Algorithm (GA), Cuckoo Optimization Algorithm (COA), Particle Swarm Optimization Algorithm (PSO) and Imperialist Competitive Algorithm (ICA) are used to compute the optimal parameters for the reward signal of BELBIC. These algorithms can select appropriate and optimal values for the parameters. These minimize the Cost Function, so the optimal values for the parameters will be founded. Selected cost function is defined to minimizing the least square errors. Cost function enforce the system errors to decay to zero rapidly. Numerical simulation results are presented to show the effectiveness of the proposed method.

Synchronization and Inverse Synchronization of Some Different Dimensional Discrete-time Chaotic Dynamical Systems via Scaling Matrices

In this paper, new types of synchronization and inverse synchro-nization are proposed for some dierent dimensional chaotic dynamical systems in discrete-time using scaling matrices. Based on Lyapunov stability theory and nonlinear controllers, new synchronization results are derived. Numerical simulations are used to verify the eectiveness of the proposed schemes.

Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos

This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS) for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, by employing the feedback control technique, necessary and sufficient criteria on CMHPS are derived. Furthermore, CMHPS between fractional-order real hyper-chaotic Rössler system and other two different dimensional fractional-order complex Lorenz-like chaotic systems is provided as two examples to discuss reduced order and increased order synchronization, respectively.

Adaptive complex modified projective synchronization of complex chaotic (hyperchaotic) systems with uncertain complex parameters

This paper introduces a new type of synchronization method of adaptive modified projective synchronization with complex scaling matrix (ACMPS) for two \(n\)-dimensional complex chaotic (hyperchaotic) systems with uncertain complex parameters. By choosing appropriate Lyapunov functions dependent on complex variables, and employing adaptive control technique, sufficient criteria on ACMPS are derived. Moreover, in the complex space, the slave system can be asymptotically synchronized up to nonidentical or identical master system by a desired complex scaling matrix, and all of unknown parameters in both master and slave systems are achieved to be identified by virtue of the complex update laws. Finally, two examples are worked out to verify the effectiveness and feasibility of the theoretical results.

Intelligent Controller for Synchronization New Three Dimensional Chaotic System

One of the most important phenomena of some systems is chaos which is caused by nonlinear dynamics. In this paper, the new 3 dimensional chaotic system is first investigated and then utilized an intelligent controller based on brain emotional learning (BELBIC), this new chaotic system is synchronized. The BELBIC consists of reward signal which accepts positive values. Improper selection of the parameters causes an improper behavior which may cause serious problems such as instability of the system. It is needed to optimize these parameters. Genetic Algorithm (GA), Cuckoo Optimization Algorithm (COA), Particle Swarm Optimization Algorithm (PSO) and Imperialist Competitive Algorithm (ICA) are used to compute the optimal parameters for the reward signal of BELBIC. These algorithms can select appropriate and optimal values for the parameters. These minimize the Cost Function, so the optimal values for the parameters will be founded. Selected cost function is defined to minimizing the least square errors. Cost function enforces the system errors to decay to zero rapidly. Numerical simulation will show that this method much better, faster and more effective than previous methods can be new 3D chaotic system mode to bring synchronized.

Function projective synchronization between four dimensional chaotic systems with uncertain parameters using modified adaptive control method

In this manuscript the function projective synchronization between different fractional order chaotic systems with uncertain parameters using modified adaptive control method is studied. The adaptive function projective synchronization controller and identification parameter laws are developed on the basis of Lyapunov stability theory. The method is successfully applied for the function projective synchronization between some fractional order chaotic systems. The analysis of the synchronization time with variations of fractional order derivatives is the key feature of the present manuscript. The numerical simulation results clearly show that the modified method is very much efficient and reliable for synchronizing the two different fractional order chaotic systems.

A Novel Four-Wing Hyperchaotic Complex System and Its Complex Modified Hybrid Projective Synchronization with Different Dimensions

We introduce a new Dadras system with complex variables which can exhibit both four-wing hyperchaotic and chaotic attractors. Some dynamic properties of the system have been described including Lyapunov exponents, fractal dimensions, and Poincaré maps. More importantly, we focus on a new type of synchronization method of modified hybrid project synchronization with complex transformation matrix (CMHPS) for different dimensional hyperchaotic and chaotic complex systems with complex parameters, where the drive and response systems can be asymptotically synchronized up to a desired complex transformation matrix, not a diagonal matrix. Furthermore, CMHPS between the novel hyperchaotic Dadras complex system and other two different dimensional complex chaotic systems is provided as an example to discuss increased order synchronization and reduced order synchronization, respectively. Numerical results verify the feasibility and effectiveness of the presented schemes.

SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS WITH TIME VARYING PARAMETERS, DISTURBANCES AND INPUT NONLINEARITIES

In this paper, the problems of robust exponential generalized and robust exponential Q-S chaos synchronization are investigated between different dimensional chaotic systems. We consider the more practical and realistic cases when unknown time varying parameters with uncertainties, environmental disturbances, and nonlinearity of input control signals are present. The adaptive technique is employed to design the appropriate controllers and the validity of the proposed controllers are proved using Lyapunov stability theorem. Furthermore, numerical simulations are performed to show the efficiency of the presented scheme.

Chaotic Image Encryption with Random Shuffling of Data

Security of valuable multimedia contents such as images in personal photograph albums, electronic publishing, frames of multicast video conference can be achieved by image encryption. Secure transmission of these contents is required to be rapid, efficient and practical. Hence, image encryption process must be chosen not only to satisfy the security goals but also to fulfill these requirements. Due to the inadequacy and inefficiency of conventional text based information encryption methods, researchers have proposed several encryption schemes. Many of them are based on chaotic algorithms. Recently, the studies are concentrated on some weaknesses of chaotic algorithms and most of the presented solutions came up with complex structured chaotic maps. In this paper, we present a self-diagonal shuffler mechanism embedded to one dimensional chaotic encryption system to overcome its leak points while keeping simplicity and efficiency properties.

Synchronization of Discrete Chaotic Systems via Double Scaling Matrix in Different Dimensions

In this paper, a new type of chaos synchronization in discrete-time is proposed when the scaling functions in Q-S synchronization are replaced by two suitable matrices. This new synchronization type allows us to study synchronization between different dimensional discrete chaotic systems in different dimensions. By using Lyapunov stability theory and nonlinear controllers, new results are derived. Numerical simulations are used to verify the effectiveness of the theoritical results and the proposed schemes derived in this paper.

Stability of Chaotic and Hyperchaotic Finance Systems

In this paper, a three (four) dimensional autonomous Finance chaotic (hyperchaotic) system is considered, and we obtained the stability of this systems. We show that the chaotic (three dimensional) system is asymptotically stable at the critical points when , and unstable otherways. While the hyperchaotic (four dimensional) system is asymptotically stable if the variables has the form . Finally, illustrative examples are given.

Passivity-based chaos control and synchronization of the four dimensional Lorenz-Stenflo system via one input

This paper discusses chaos control and synchronization of the four dimensional Lorenz-Stenflo system based on passive control technique. Using passive theory, chaos control and synchronization of a four dimensional Lorenz-Stenflo chaotic system are realized with one input. The designed controllers ensure the stability of the controlled system and error dynamical system between two identical Lorenz-Stenflo systems. Also, the controllers ensure that the controlled system and error dynamical system converge to zero equilibrium. Numerical simulations show that the proposed method is effective for the Lorenz-Stenflo system.

Streamwise-Localized Solutions at the Onset of Turbulence in Pipe Flow

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent transients arise from one such solution branch.

Encryption algorithm based on double chaos system with mutual feedback

In order to increase the security of the low dimensional chaotic encryption system while not affecting the performance,a composite chaotic encryption system based on Logistic mapping and Tent mapping was presented.Firstly,the secret-key sequences were generated based on two mapping with mutual feedback,which was used to encrypt the plaintext;at the same time,the number of chaotic iterations was changed through cipher-feedback,and the iterative process has certain randomness.The results show,compared with single Logistic chaotic encryption,the algorithm not only has a large key space,high encryption intension and good operation efficiency of low dimensional chaotic encryption system,but also can resist brute-force attack,statistical attack and phase diagrams attack effectively.

Adaptive generalized function projective synchronization of uncertain chaotic complex systems

The complex nonlinear systems appear in many important fields of physics and engineering, which are very useful for cryptography and secure communication. This paper investigates adaptive generalized function projective synchronization (AGFPS) between two different dimensional chaotic complex systems with fully or partially unknown parameters via both reduced order and increased order. Based on the Lyapunov stability theorem and adaptive control technique, a general adaptive controller with corresponding parameter update rule is constructed to achieve AGFPS between two nonidentical chaotic complex systems with distinct orders, and identify the unknown parameters simultaneously. This scheme is then applied to obtain AGFPS between the hyperchaotic complex Lu system and the chaotic complex Lorenz system with fully unknown parameters, and between the uncertain chaotic complex Chen system and the uncertain hyperchaotic complex Lorenz system, respectively. Corresponding simulations results are performed to show the feasibility and effectiveness of the proposed synchronization method.

Triple mode alignment in a canonical model of the blue-sky catastrophe

The blue-sky catastrophe (BSC) is a homoclinic bifurcation of a saddle node periodic orbit of codimension one, which has been found to occur in a number of physically relevant dynamics systems. The onset and termination of the BSC in a chaotic system is shown to coincide with the occurrence of triple mode alignment in a canonical model undergoing the BSC when the model is recast as an oscillator system. Typically, such behavior is only seen in hyperchaotic systems of dimension greater than three. Hence, in the case of three dimensional chaotic systems, competitive modes may under some circumstances be used in the prediction of the blue-sky catastrophe. Limitations to this approach are also discussed.

Hybrid robust modified function projective lag synchronization in two different dimensional chaotic systems

In this article, a novel synchronization scheme, modified function projective lag synchronization (MFPLS) in two different dimensional chaotic systems with parameter perturbations, is proposed. In the proposed method, the states of two nonidentical chaotic systems with different orders are asymptotically lag synchronized up to a desired scaling function matrix by means of reduced order and increased order, respectively. Furthermore, based on the reality situation, the parameter perturbations are involved, which are assumed to appear in both drive and response systems. With the Lyapunov stability theory, an adaptive controller is designed to achieve MFPLS. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

Modified Function Projective Synchronization of Fractional Order Chaotic Systems with Different Dimensions

The modified function projective synchronization of different dimensional fractional-order chaotic systems with known or unknown parameters is investigated in this paper. Based on the stability theorem of linear fractional-order systems, the adaptive controllers with corresponding parameter update laws for achieving the synchronization are given. The fractional-order chaotic system and hyperchaotic system are applied to achieve synchronization in both reduced order and increased order. The corresponding numerical results coincide with theoretical analysis.

Predictability and chaotic nature of daily streamflow

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation dimension method (Grassberger-Procaccia algorithm) and false nearest neighbour method. Embedding dimensions of 6-7 obtained, indicate the possible presence of low-dimensional chaotic behaviour. The predictability of the system is estimated by calculating the system's Lyapunov exponent. A positive maximum Lyapunov exponent of 0.167 indicates that the system is chaotic and unstable with a maximum predictability of only 6 days. These results give a positive indication towards considering streamflow as a low dimensional chaotic system than as a stochastic system. Prediction is done using local polynomial method for a range of embedding dimensions and delay times. The uncertainty in the chaotic streamflow series is reasonably captured through the ensemble approach using local polynomial method.

Predictability and Chaotic Nature of Daily Streamflow

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation dimension method (Grassberger-Procaccia algorithm) and false nearest neighbour method. Embedding dimensions of 6-7 obtained, indicate the possible presence of low-dimensional chaotic behaviour. The predictability of the system is estimated by calculating the system’s Lyapunov exponent. A positive maximum Lyapunov exponent of 0.167 indicates that the system is chaotic and unstable with a maximum predictability of only 6 days. These results give a positive indication towards considering streamflow as a low dimensional chaotic system than as a stochastic system. Prediction is done using local polynomial method for a range of embedding dimensions and delay times. The uncertainty in the chaotic streamflow series is reasonably captured through the ensemble approach using local polynomial method.