Dynamics analysis and cryptographic implementation of a fractional-order memristive cellular neural network model

Due to the fact that a memristor with memory properties is an ideal electronic component for implementation of the artificial neural synaptic function,a brand-new tristable locally active memristor model is first proposed in this paper.Here,a novel four-dimensional fractional-order memristive cellular neural network(FO-MCNN)model with hidden attractors is constructed to enhance the engineering feasibility of the original CNN model and its performance.Then,its hardware circuit implementation and complicated dynamic properties are investigated on multi-simulation platforms.Subsequently,it is used toward secure communication application scenarios.Taking it as the pseudo-random number generator(PRNG),a new privacy image security scheme is designed based on the adaptive sampling rate compressive sensing(ASR-CS)model.Eventually,the simulation analysis and comparative experiments manifest that the proposed data encryption scheme possesses strong immunity against various security attack models and satisfactory compression performance.

Design of multilayer cellular neural network based on memristor crossbar and its application to edge detection

Memristor with memory properties can be applied to connection points(synapses)between cells in a cellular neural network(CNN).This paper highlights memristor crossbar-based multilayer CNN(MCM-CNN)and its application to edge detection.An MCM-CNN is designed by adopting a memristor crossbar composed of a pair of memristors.MCM-CNN based on the memristor crossbar with changeable weight is suitable for edge detection of a binary image and a color image considering its characteristics of programmablization and compactation.Figure of merit(FOM)is introduced to evaluate the proposed structure and several traditional edge detection operators for edge detection results.Experiment results show that the FOM of MCM-CNN is three times more than that of the traditional edge detection operators.

Chaotic phenomena in Josephson circuits coupled quantum cellular neural networks

In this paper the nonlinear dynamical behaviour of a quantum cellular neural network （QCNN） by coupling Josephson circuits was investigated and it was shown that the QCNN using only two of them can cause the onset of chaotic oscillation. The theoretical analysis and simulation for the two Josephson-circuits-coupled QCNN have been done by using the amplitude and phase as state variables. The complex chaotic behaviours can be observed and then proved by calculating Lyapunov exponents. The study provides valuable information about QCNNs for future application in high-parallel signal processing and novel chaotic generators.

Global exponential stability of mixed discrete and distributively delayed cellular neural network

This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.

The characteristics of nonlinear chaotic dynamics in quantum cellular neural networks

With the polarization of quantum-dot cell and quantum phase serving as state variables, this paper does both theoretical analysis and simulation for the complex nonlinear dynamical behaviour of a three-cell-coupled Quantum Cellular Neural Network （QCNN）, including equilibrium points, bifurcation and chaotic behaviour. Different phenomena, such as quasi-periodic, chaotic and hyper-chaotic states as well as bifurcations are revealed. The system＇s bifurcation and chaotic behaviour under the influence of the different coupling parameters are analysed. And it finds that the unbalanced cells coupled QCNN is easy to cause chaotic oscillation and the system response enters into chaotic state from quasi-periodic state by quasi-period bifurcation; however, the balanced cells coupled QCNN also can be chaotic when coupling parameters is in some region. Additionally, both the unbalanced and balanced cells coupled QCNNs can possess hyper-chaotic behaviour. It provides valuable information about QCNNs for future application in high-parallel signal processing and novel ultra-small chaotic generators.

One-way hash function based on hyper-chaotic cellular neural network

The design of an efficient one-way hash function with good performance is a hot spot in modern cryptography researches. In this paper, a hash function construction method based on cell neural network with hyper-chaos characteristics is proposed. First, the chaos sequence is gotten by iterating cellular neural network with Runge Kutta algorithm, and then the chaos sequence is iterated with the message. The hash code is obtained through the corre- sponding transform of the latter chaos sequence. Simulation and analysis demonstrate that the new method has the merit of convenience, high sensitivity to initial values, good hash performance, especially the strong stability.

Exponential stability for cellular neural networks: an LMI approach

A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks （DCNNs） is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.

Stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks with mixed delays and the Wiener process based on sampled-data control

We investigate the stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks （MJFCNNs） with discrete, unbounded distributed delays, and the Wiener process based on sampled-data control using the linear matrix inequality （LMI） approach. The Lyapunov–Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach is employed to derive several sufficient criteria in terms of LMIs to ensure that the delayed MJFCNNs with the Wiener process is stochastic asymptotical synchronous. Restrictions （e.g., time derivative is smaller than one） are removed to obtain a proposed sampled-data controller. Finally, a numerical example is provided to demonstrate the reliability of the derived results.

Anti-windup compensation design for a class of distributed time-delayed cellular neural networks

Both time-delays and anti-windup(AW)problems are conventional problems in system design,which are scarcely discussed in cellular neural networks(CNNs).This paper discusses stabilization for a class of distributed time-delayed CNNs with input saturation.Based on the Lyapunov theory and the Schur complement principle,a bilinear matrix inequality(BMI)criterion is designed to stabilize the system with input saturation.By matrix congruent transformation,the BMI control criterion can be changed into linear matrix inequality(LMI)criterion,then it can be easily solved by the computer.It is a one-step AW strategy that the feedback compensator and the AW compensator can be determined simultaneously.The attraction domain and its optimization are also discussed.The structure of CNNs with both constant timedelays and distribute time-delays is more general.This method is simple and systematic,allowing dealing with a large class of such systems whose excitation satisfies the Lipschitz condition.The simulation results verify the effectiveness and feasibility of the proposed method.

Global exponential stability for delayed cellular neural networks and estimate of exponential convergence rate

Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.

A Study of Cellular Neural Networks with Vertex-Edge Topological Descriptors

The CellularNeuralNetwork(CNN)has various parallel processing applications,image processing,non-linear processing,geometric maps,highspeed computations.It is an analog paradigm,consists of an array of cells that are interconnected locally.Cells can be arranged in different configurations.Each cell has an input,a state,and an output.The cellular neural network allows cells to communicate with the neighbor cells only.It can be represented graphically;cells will represent by vertices and their interconnections will represent by edges.In chemical graph theory,topological descriptors are used to study graph structure and their biological activities.It is a single value that characterizes the whole graph.In this article,the vertex-edge topological descriptors have been calculated for cellular neural network.Results can be used for cellular neural network of any size.This will enhance the applications of cellular neural network in image processing,solving partial differential equations,analyzing 3D surfaces,sensory-motor organs,and modeling biological vision.

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.

Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays

In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.

Stability for Cellular Neural Networks with Delay

The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixand theω?limit set. It is shown that the new conditions are not related to the delayed parameter.

Modeling of Trophospheric Ozone Concentrations Using Genetically Trained Multi-Level Cellular Neural Networks

Tropospheric ozone concentrations, which are an important air pollutant, are modeled by the use of an artificial intelligence structure. Data obtained from air pollution measurement stations in the city of Istanbul are utilized in constituting the model. A supervised algorithm for the evaluation of ozone concentration using a genetically trained multi-level cellular neural network （ML-CNN） is introduced, developed, and applied to real data. A genetic algorithm is used in the optimization of CNN templates. The model results and the actual measurement results are compared and statistically evaluated. It is observed that seasonal changes in ozone concentrations are reflected effectively by the concentrations estimated by the multilevel-CNN model structure, with a correlation value of 0.57 ascertained between actual and model results. It is shown that the multilevel-CNN modeling technique is as satisfactory as other modeling techniques in associating the data in a complex medium in air pollution applications.

Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

Fuzzy cellular neural networks （FCNNs） are special kinds of cellular neural networks （CNNs）. Each cell in an FCNN contains fuzzy operating abilities. The entire network is governed by cellular computing laws. The design of FCNNs is based on fuzzy local rules. In this paper, a linear matrix inequality （LMI） approach for synchronization control of FCNNs with mixed delays is investigated. Mixed delays include discrete time-varying delays and unbounded distributed delays. A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network. By constructing the Lyapunov-Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs. The controller can be easily obtained by solving the derived LMIs. A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method.

Exponential stability of cellular neural networks with multiple time delays and impulsive effects

In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.

Global exponential stability analysis of cellular neural networks with multiple time delays

Global exponential stability problems are investigated for cellular neural networks （CNN） with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.

Attractors and the attraction basins of discrete-time cellular neural networks

The dynamic behavior of discrete-time cellular neural networks(DTCNN), which is strict with zero threshold value, is mainly studied in asynchronous mode and in synchronous mode. In general, a k-attractor of DTCNN is not a convergent point. But in this paper, it is proved that a k-attractor is a convergent point if the strict DTCNN satisfies some conditions. The attraction basin of the strict DTCNN is studied, one example is given to illustrate the previous conclusions to be wrong, and several results are presented. The obtained results on k-attractor and attraction basin not only correct the previous results, but also provide a theoretical foundation of performance analysis and new applications of the DTCNN.

Stability analysis of cellular neural networks with time-varying delay

The global asymptotic stability of cellular neural networks with delays is investigated. Three kinds of time delays have been considered. New delay-dependent stability criteria are proposed and are formulated as the feasibility of some linear matrix inequalities, which can be checked easily by resorting to the recently developed interior-point algorithms. Based on the Finsler Lemma, it is theoretically proved that the proposed stability criteria are less conservative than some existing results.