An asymmetric image cryptosystem based on the adaptive synchronization of an uncertain unified chaotic system and a cellular neural network

Chaotic dynamics provide a fast and simple means to create an excellent image cryptosystem, because it is extremely sensitive to initial conditions and system parameters, pseudorandomness, and non-periodicity. However, most chaos-based image encryption schemes are symmetric cryptographic techniques, which have been proven to be more vulnerable, compared to an asymmetric cryptosystem. This paper develops an asymmetric image cryptosystem, based on the adaptive synchronization of two different chaotic systems, namely a unified chaotic system and a cellular neural network. An adaptive controller with parameter update laws is formulated, using the Lyapunov stability theory, to asymptotically synchronize the two chaotic systems. The synchronization controller is embedded in the image cryptosystem and generates a pair of asymmetric keys, for image encryption and decryption. Using numerical simulations, three sets of experiments are conducted to evaluate the feasibility and reliability of the proposed chaos-based image cryptosystem.     

Synchronization control for the competitive complex networks with time delay and stochastic effects

The synchronization control problem for the competitive complex network with time delay and stochastic effects is investigated by using the stochastic technique and Lyapunov stability theory. The competitive complex network means that the dynamical varying rate of a part of nodes is faster than other nodes. Some synchronization criteria are derived by the full controller and pinning controller, respectively, and these criteria are convenient to be used for concision. A numerical example is provided to illustrate the effectiveness of the method proposed in this paper.     

Fixed-time synchronization of a reaction-diffusion BAM neural network with distributed delay and its application to image encryption

In this paper, the fixed-time synchronization of reaction-diffusion BAM neural networks is investigated, where both discrete and distributed delays are taken into account. Combining Lyapunov stability theory and several integral inequalities, fixed-time synchronization criteria are established. Through sensitivity analysis, we find the key controller parameters that have a great influence on the maximum settling time. Using the chaotic sequences generated by the neural network, the color image can be encrypted by the Arnold Cat Map and the pixel diffusion. Experiments show that the image encryption algorithm designed in this paper has good properties of security and anti-attacking, which meets the requirements for the secure transmission of image information.     

Synchronization for stochastic hybrid coupled controlled systems with Lévy noise

In this paper, synchronization for stochastic hybrid-delayed coupled systems with Lévy noise on a network (SHDCLN) is investigated via aperiodically intermittent control. Here time delays, Markovian switching and Lévy noise are considered on a network simultaneously for the first time. After that, by means of Lyapunov method, graph theory, and some techniques of inequality, some sufficient conditions are derived to guarantee the synchronization for SHDCLN. In addition, the designed range of aperiodically intermittent controller parameters is shown. Meanwhile, the coupling strength and the perturbed intensity of noise have a great impact on the intensity of control. Then, we investigate synchronization for stochastic hybrid delayed Chua's circuits with Lévy noise on a network as a practical application of our theoretical results. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.     

Sliding mode synchronization controller design with neural network for uncertain chaotic systems

A sliding mode synchronization controller is presented with RBF neural network for two chaotic systems in this paper. The compound disturbance of the synchronization error system consists of nonlinear uncertainties and exterior disturbances of chaotic systems. Based on RBF neural networks, a compound disturbance observer is proposed and the update law of parameters is given to monitor the compound disturbance. The synchronization controller is given based on the output of the compound disturbance observer. The designed controller can make the synchronization error convergent to zero and overcome the disruption of the uncertainty and the exterior disturbance of the system. Finally, an example is given to demonstrate the availability of the proposed synchronization control method.     

Circuit realization,chaos synchronization and estimation of parameters of a hyperchaotic system with unknown parameters

In this article, the adaptive chaos synchronization technique is implemented by an electronic circuit and applied to the hyperchaotic system proposed by Chen et al. We consider the more realistic and practical case where all the parameters of the master system are unknowns. We propose and implement an electronic circuit that performs the estimation of the unknown parameters and the updating of the parameters of the slave system automatically, and hence it achieves the synchronization. To the best of our knowledge, this is the first attempt to implement a circuit that estimates the values of the unknown parameters of chaotic system and achieves synchronization. The proposed circuit has a variety of suitable real applications related to chaos encryption and cryptography. The outputs of the implemented circuits and numerical simulation results are shown to view the performance of the synchronized system and the proposed circuit.     

Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control

In this paper, the problem of guaranteed cost synchronization for a complex network is investigated. In order to achieve the synchronization, two types of guaranteed cost dynamic feedback controller are designed. Based on Lyapunov stability theory, a linear matrix inequality (LMI) convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function. Finally, a numerical example is given to illustrate the proposed method.     

Adaptive synchronization of drive-response fractional-order complex dynamical networks with uncertain parameters

This paper investigates the adaptive synchronization in the drive-response fractional-order dynamical networks with uncertain parameters. By means of both the stability theory of fractional-order differential system and the adaptive control technique, a novel adaptive synchronization controller is developed with a more general and simpler analytical expression, which does not contain the parameters of the complex network, and effective adaptive laws of parameters. Furthermore, the very strong and conservative uniformly Lipschitz condition on the node dynamics of complex network is released. To demonstrate the validity of the proposed method, the examples for the synchronization of systems with the chaotic and hyper-chaotic node dynamics are presented.     

Cluster synchronization for directed community networks via pinning partial schemes

In this paper, we focus on driving a class of directed networks to achieve cluster synchronization by pinning schemes. The desired cluster synchronization states are no longer decoupled orbits but a set of un-decoupled trajectories. Each community is considered as a whole and the synchronization criteria are derived based on the information of communities. Several pinning schemes including feedback control and adaptive strategy are proposed to select controlled communities by analyzing the information of each community such as indegrees and outdegrees. In all, this paper answers several challenging problems in pinning control of directed community networks: (1) What communities should be chosen as controlled candidates? (2) How many communities are needed to be controlled? (3) How large should the control gains be used in a given community network to achieve cluster synchronization? Finally, an example with numerical simulations is given to demonstrate the effectiveness of the theoretical results.     

Robust synchronization of chaotic behavior in unidirectional coupled RCLSJ models subject to uncertainties

This paper deals with the problem of robust synchronization for a class of unidirectional coupled RCL-shunted Josephson junction (RCLSJ) models. A nonlinear controller is proposed based on variable structure control technique to ensure that these coupled RCLSJ models with different parameters can be asymptotically synchronized even when uncertainties are present in the coupled system. Finally, a comparative example is given to emphasize the simplicity and robustness of the proposed method.     

Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems

In this paper, a robust adaptive neural network synchronization controller is proposed for two chaotic systems with input time delay and uncertainty. The studied chaotic system may possess a wide class of nonlinear time-delayed input uncertainty. The radial basis function (RBF) neural network is used to approximate the unknown continuous bounded function item of the time delay uncertainty via appropriate weight value updated law. With the output of RBF neural network, a robust adaptive synchronization control scheme is presented for the time delay uncertain chaotic system. Finally, a simulation example is used to illustrate the effectiveness of the proposed synchronization control scheme.     

Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros

Under the existence of system uncertainties, external disturbances, and input nonlinearity, complete synchronization and anti-synchronization between two chaotic gyros are achieved by introducing a novel adaptive terminal sliding mode (ATSM) controller. In the literature, by taking account of input nonlinearity, the magnitudes of bounded nonlinear dynamics of synchronous error system were required in the designed sliding mode controller. In this study, the proposed ATSM controller associated with time-varying feedback gains can tackle nonlinear dynamics according to the novel adaptive rules. These feedback gains are not necessary to be determined in advance but updated by the adaptive rules without known the magnitudes of bounded nonlinear dynamics, system uncertainties, and external disturbances. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem, and the numerical simulations are performed to verify the effectiveness of presented schemes.     

Projective lag synchronization of the general complex dynamical networks with distinct nodes

In this paper, projective lag synchronization of the general complex dynamical networks with different nodes is investigated. Combining Barbalat’s lemma with adaptive control technique, the adaptive feedback controllers are constructed to achieve projective lag synchronization between the dynamical network with diverse nodes and arbitrary desired trajectory. The presented synchronization method can be applied to any complex networks. It is discovered that the update gains, the time delay, the network size and the network topology have influence on the synchronization effect. Furthermore, projective lag synchronization of the dynamical networks can still be efficiently realized in presence of noise and parameter perturbations. Corresponding numerical simulations are performed to validate the effectiveness and robustness of the proposed synchronization scheme.     

A geometric view on learning Bayesian network structures

We recall the basic idea of an algebraic approach to learning Bayesian network (BN) structures, namely to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices (=extreme points) of a certain polytope. Motivated by the geometric view, we introduce the concept of the geometric neighborhood for standard imsets, and, consequently, for BN structures. Then we show that it always includes the inclusion neighborhood, which was introduced earlier in connection with the greedy equivalence search (GES) algorithm. The third result is that the global optimum of an affine function over the polytope coincides with the local optimum relative to the geometric neighborhood.To illustrate the new concept by an example, we describe the geometric neighborhood in the case of three variables and show it differs from the inclusion neighborhood. This leads to a simple example of the failure of the GES algorithm if data are not “generated” from a perfectly Markovian distribution. The point is that one can avoid this failure if the search technique is based on the geometric neighborhood instead. We also found out what is the geometric neighborhood in the case of four and five variables.     

Multi-variable control of chaos using PSO-based minimum entropy control

The minimum entropy (ME) control is a chaos control technique which causes chaotic behavior to vanish by stabilizing unstable periodic orbits of the system without using mathematical model of the system. In this technique some controller type, normally delayed feedback controller, with an adjustable parameter such as feedback gain is used. The adjustable parameter is determined such that the entropy of the system is minimized. Proposed in this paper is the PSO-based multi-variable ME control. In this technique two or more control parameters are adjusted concurrently either in a single or in multiple control inputs. Thus it is possible to use two or more feedback terms in the delayed feedback controller and adjust their gains. Also the multi-variable ME control can be used in multi-input systems. The minimizing engine in this technique is the particle swarm optimizer. Using online PSO, the PSO-based multi-variable ME control technique is applied to stabilize the 1-cycle fixed points of the Logistic map, the Hénon map, and the chaotic Duffing system. The results exhibit good effectiveness and performance of this controller.     

Output-feedback synchronization of chaotic systems based on sum-of-squares approach

This paper investigates the synchronization of chaotic systems using an output feedback polynomial controller. As only output system states are considered, it makes the controller design and system analysis more challenging compared to the full-state feedback control schemes. To study the system stability and synthesize the output feedback polynomial controller, Lyapunov stability theory is employed. Sufficient stability conditions are derived in terms of sum of squares (SOS) conditions to guarantee the system stability and aid the controller synthesis. A genetic algorithm-based SOS technique is proposed to find the solution to the SOS conditions and the parameter values of the output feedback polynomial controller. A simulation example is employed to illustrate the effectiveness of the proposed approach.     

Quantized adaptive pinning control for fixed/preassigned-time cluster synchronization of multi-weighted complex networks with stochastic disturbances

The article studies preassigned-time (PAT) and fixed-time (FXT) cluster synchronization of multi-weighted complex networks (CNs) with stochastic disturbances through designing quantized adaptive pinning control scheme. Firstly, the controller can achieve lower control costs and save communication channels. By designing a novel and appropriate Lyapunov function, combining the characteristics of Wiener process and utilizing a method of comparison system, FXT synchronization criteria of CNs are proposed. The FXT criteria can be more widely applied in directed and undirected multi-weighted CNs. Besides, the PAT cluster synchronization is also investigated by utilizing a novel control scheme that the gains of controller are finite, where the synchronization time can be preassigned based on realistic situation. The effectiveness of theoretical results is illustrated via simulations.     

Exponential synchronization of chaotic systems subject to uncertainties in the control input

A sliding mode control technique is introduced for exponential synchronization of chaotic systems. These systems are described by a general form including matched and unmatched nonlinear functions. A new hitting-free switching surface of proportional-integral type is proposed. This type of switching surface is without the hitting process if the attraction of sliding manifold is ensured. This property makes it easy to exponentially synchronize the master-slave chaotic systems. Based on this switching surface, a robust sliding mode controller (SMC) is derived to guarantee the attraction of sliding manifold even when the system is subjected to input uncertainties. An example is included to illustrate the results developed in this paper.     

Projective Synchronization of Fractional Quaternion Neural Networks With Time-Varying Delays北大核心CSCD

研究了具有时变时滞的分数阶四元数神经网络的投影同步问题.该文不将分数阶四元数神经网络系统转化成两个复值系统或四个实值系统,而是将四元数系统当做一个整体进行处理.在合适的控制器下,通过构造合适的Lyapunov函数,并利用一些不等式技巧,得到了具有时变时滞分数阶四元数时滞神经网络投影同步的充分性判据.最后,通过数值仿真实例验证了所得结论的有效性和可行性.     

Single impulsive controller for globally exponential synchronization of dynamical networks

This paper is devoted to studying the synchronization control of impulsive dynamical networks. A single impulsive controller is proved to be effective for the stabilization of dynamical networks with impulse-coupling. Some simple and easily verified criteria are given for the stabilization of impulsive dynamical networks under a single impulsive controller and/or a single negative state-feedback control. Moreover, the effects of a single impulsive controller, a single state-feedback controller and an isolated dynamical system on the synchronization process are respectively distilled and explicitly expressed in the derived criteria. The structure of the dynamical network can be directed and weakly connected with a rooted spanning tree. Moreover, the convergence rate of the dynamical network is also explicitly estimated, and there is no requirement on the lower and upper bounds of the impulsive intervals. A numerical example is presented to illustrate the efficiency of the designed controller and the validity of the analytical results.