Control of a fractional chaotic system based on a fractional-order resistor-capacitor filter

We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional- order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method.

Modified impulsive synchronization of fractional order hyperchaotic systems

In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.

A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system

This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By intro- ducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.

The stability control of fractional order unified chaotic system with sliding mode control theory

This paper studies the stability of the fractional order unified chaotic system with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for the fractional order unified chaotic system. By the existing proof of sliding manifold, the sliding mode controller is designed. To improve the convergence rate, the equivalent controller includes two parts： the continuous part and switching part. With Gronwall＇s inequality and the boundness of chaotic attractor, the finite stabilization of the fractional order unified chaotic system is proved, and the controlling parameters can be obtained. Simulation results are made to verify the effectiveness of this method.

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bifurcation diagrams,the largest Lyapunov exponent plot,and the phase portraits are derived,respectively.Finally,with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem,we apply the discrete fractional map into color image encryption.After that,the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.

Adaptive lag synchronization and parameter identification of fractional order chaotic systems

This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unknown parameters are identified by using the adaptive lag laws. Moreover, the scheme is analytical and is simple to implement in practice. The well-known fractional order chaotic L/i system is used to illustrate the validity of this theoretic method.

Video Transmission Secrecy Improvement Based on Fractional Order Hyper Chaotic System

In the Digital World scenario,the confidentiality of information in video transmission plays an important role.Chaotic systems have been shown to be effective for video signal encryption.To improve video transmission secrecy,compressive encryption method is proposed to accomplish compression and encryption based on fractional order hyper chaotic system that incorporates Compressive Sensing(CS),pixel level,bit level scrambling and nucleotide Sequences operations.The measurement matrix generates by the fractional order hyper chaotic system strengthens the efficiency of the encryption process.To avoid plain text attack,the CS measurement is scrambled to its pixel level,bit level scrambling decreases the similarity between the adjacent measurements and the nucleotide sequence operations are done on the scrambled bits,increasing the encryption.Two stages are comprised in the reconstruction technique,the first stage uses the intra-frame similarity and offers robust preliminary retrieval for each frame,and the second stage iteratively improves the efficiency of reconstruction by integrating inter frame Multi Hypothesis(MH)estimation and weighted residual sparsity modeling.In each iteration,the residual coefficient weights are modified using a mathematical approach based on the MH predictions,and the Split Bregman iteration algorithm is defined to resolve weighted l1 regularization.Experimental findings show that the proposed algorithm provides good compression of video coupled with an efficient encryption method that is resistant to multiple attacks.

Fractional Chaos Based Communication Systems——An Introduction

As one of secure communication means, chaotic communication systems has been well-developed during the past three decades. Technical papers, both for theoretical and practical investigations, have reached a huge amount in number. On the other hand, fractional chaos, as a parallel ongoing research topic, also attracts many researchers to investigate. As far as the IT field is concerned, the research on control systems by using fractional chaos known as FOC （fractional order control） has been a hot issue for quite a long time. As a comparison, interesting enough, up to now we have not found any research result related to Fractional Chaos Communi- cation （FCC） system, i.e., a system based on fractional chaos. The motivation of the present article is to reveal the feasibility of realizing communication systems based upon FCC and their superiority over the conventional integer chaotic communication systems. Principles of FCC and its advantages over integer chaotic communication systems are also discussed.

Similarity Analytic Solutions of a 3D-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function

The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.

An Efficient Three-Factor Authenticated Key Agreement Technique Using FCM Under HC-IoT Architectures

The Human-Centered Internet of Things(HC-IoT)is fast becoming a hotbed of security and privacy concerns.Two users can establish a common session key through a trusted server over an open communication channel using a three-party authenticated key agreement.Most of the early authenticated key agreement systems relied on pairing,hashing,or modular exponentiation processes that are computationally intensive and cost-prohibitive.In order to address this problem,this paper offers a new three-party authenticated key agreement technique based on fractional chaotic maps.The new scheme uses fractional chaotic maps and supports the dynamic sensing of HC-IoT devices in the network architecture without a password table.The projected security scheme utilized a hash function,which works well for the resource-limited HC-IoT architectures.Test results show that our new technique is resistant to password guessing attacks since it does not use a password.Furthermore,our approach provides users with comprehensive privacy protection,ensuring that a user forgery attack causes no harm.Finally,our new technique offers better security features than the techniques currently available in the literature.