Chaotic Hopfield Neural Network Research Articles

An image encryption algorithm based on a 3D chaotic Hopfield neural network and random row–column permutation

This study proposes a novel color image encryption algorithm based on a 3D chaotic Hopfield neural network and random row–column permutation. First, a 3D chaotic Hopfield neural network is proposed to produce the random sequence for generating the diffusion and permutation keys. Then, the rows and columns of the original image are randomly arranged according to the permutation key in the permutation process. Three subgraphs are formed by separating the R, G, and B components of the color image in the diffusion process. Each of the three subgraphs is split along the columns to form three parts; the left and middle parts are exchanged. Three diffusion keys are used to encrypt each of the three parts. Finally, the individually encrypted subgraphs are stitched together to obtain the final encrypted image. Simulation results using MATLAB and FPGA and security analysis demonstrate that the encryption scheme has good performance.

An Optical Image Encryption Method Using Hopfield Neural Network.

In this paper, aiming to solve the problem of vital information security as well as neural network application in optical encryption system, we propose an optical image encryption method by using the Hopfield neural network. The algorithm uses a fuzzy single neuronal dynamic system and a chaotic Hopfield neural network for chaotic sequence generation and then obtains chaotic random phase masks. Initially, the original images are decomposed into sub-signals through wavelet packet transform, and the sub-signals are divided into two layers by adaptive classification after scrambling. The double random-phase encoding in 4f system and Fresnel domain is implemented on two layers, respectively. The sub-signals are performed with different conversions according to their standard deviation to assure that the local information’s security is guaranteed. Meanwhile, the parameters such as wavelength and diffraction distance are considered as additional keys, which can enhance the overall security. Then, inverse wavelet packet transform is applied to reconstruct the image, and a second scrambling is implemented. In order to handle and manage the parameters used in the scheme, the public key cryptosystem is applied. Finally, experiments and security analysis are presented to demonstrate the feasibility and robustness of the proposed scheme.

Analysis and control of the fractional chaotic Hopfield neural network

The fractional Hopfield neural network (HNN) model is studied here analyzing its symmetry, uniqueness of the solution, dissipativity, fixed points etc. A Lyapunov and bifurcation analysis of the system is done for specific as well as variable fractional order. Since a very long time ago, HNN has been carefully studied and applied in various fields. Because of the exceptional non-linearity of the neuron activation function, the HNN system is stoutly non-linear. Chaos control using adaptive SMC considering disturbances and uncertainties is done about randomly chosen points by designing suitable controllers. Numerical simulations performed in MATLAB verify the efficacy of the designed controllers.

Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks

The study focuses on the chaotic behavior of a three-dimensional Hopfield neural network with time delay. We find the aspecific coefficient matrix and the initial value condition of the system and use MATLAB software to draw its graph. The result shows that their shape is very similar to the figure of Roslerʼs chaotic system. Furthermore, we analyzed the divergence, the eigenvalue of the Jacobian matrix for the equilibrium point, and the Lyapunov exponent of the system. These properties prove that the system does have chaotic behavior. This result not only confirms that there is chaos in the neural networks but also that the chaotic characteristics of the system are very similar to those of Roslerʼs chaotic system under certain conditions. This discovery provides useful information that can be applied to other aspects of chaotic Hopfield neural networks, such as chaotic synchronization and control.

Two-stage data encryption using chaotic neural networks

Securing a wireless sensor system is a hard task for researchers today. Strengthening the authentication system before connection establishment is the right way to enhance the architecture and also to provide secured communication from eavesdroppers. In this paper, we present a novel algorithm to enhance the security of data using a hybrid model which uses an adaptive encoding technique alongside Chaotic Hopfield Neural Network. The proposed computation upgrades the security of a key shared between any nodes. Our experimental results show that the security of transmitted data is better than traditional algorithms. Moreover, we also show that the computational time for the proposed algorithm is less than known traditional algorithms.

Domain-Structured Chaos in a Hopfield Neural Network

In this paper, we provide a new method for constructing chaotic Hopfield neural networks. Our approach is based on structuring the domain to form a special set through the discrete evolution of the network state variables. In the chaotic regime, the formed set is invariant under the system governing the dynamics of the neural network. The approach can be viewed as an extension of the unimodality technique for one-dimensional map, thereby generating chaos from higher-dimensional systems. We show that the discrete Hopfield neural network considered is chaotic in the sense of Devaney, Li–Yorke, and Poincaré. Mathematical analysis and numerical simulation are provided to confirm the presence of chaos in the network.

Coexisting Behaviors of Asymmetric Attractors in Hyperbolic-Type Memristor based Hopfield Neural Network.

A new hyperbolic-type memristor emulator is presented and its frequency-dependent pinched hysteresis loops are analyzed by numerical simulations and confirmed by hardware experiments. Based on the emulator, a novel hyperbolic-type memristor based 3-neuron Hopfield neural network (HNN) is proposed, which is achieved through substituting one coupling-connection weight with a memristive synaptic weight. It is numerically shown that the memristive HNN has a dynamical transition from chaotic, to periodic, and further to stable point behaviors with the variations of the memristor inner parameter, implying the stabilization effect of the hyperbolic-type memristor on the chaotic HNN. Of particular interest, it should be highly stressed that for different memristor inner parameters, different coexisting behaviors of asymmetric attractors are emerged under different initial conditions, leading to the existence of multistable oscillation states in the memristive HNN. Furthermore, by using commercial discrete components, a nonlinear circuit is designed and PSPICE circuit simulations and hardware experiments are performed. The results simulated and captured from the realization circuit are consistent with numerical simulations, which well verify the facticity of coexisting asymmetric attractors' behaviors.

Novel improved blind detection algorithms based on chaotic neural networks

In this paper we apply the transiently chaotic Hopfield neural networks (TCHNN) to the blind signal detection algorithm with BPSK signals and solve multi-start problem of Hopfield neural networks (HNN). And in this paper we propose an improved algorithm of double sigmoid transiently chaotic Hopfield neural networks (DS-TCHNN) on the basis of TCHNN, construct a new energy function of DS-TCHNN, and prove the stability of DS-TCHNN in asynchronous update mode and synchronous update mode. Simulation results show that TCHNN can skip local minima and has better anti-noise performance than HNN. While, DS-TCHNN inherits all the advantages of TCHNN and its speed of convergence is fast. Besides, DS-TCHNN needs shorter data to reach a global true equilibrium point so that the computational complexity is reduced and the running time is shortened.

An Improved Block Cryptosystem Based on Iterating Delayed Chaotic Neural Networks

Recently, a large number of chaotic cryptosystems have been proposed, many of them fundamentally flawed by lack of robustness and security. In this paper, we point out the weakness of a very recent block cipher algorithm which is based on the chaotic Hopfield neural networks with time varying delay and give the improved scheme of it. We provide the chosen plaintext attack to recover the permuted plaintext string, and point out that the encryption speed is not fast enough. It is shown that the dependence on the key, but not on the plaintext, to generate binary sequences of iterating the chaotic map mechanism facilitates leakage of the information and vulnerable been attacked. Based on such a fact, we give the improved scheme to obtain higher security and faster speed.

Synchronization of a Class of Fractional-Order Chaotic Neural Networks

The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. The synchronization condition is easy to verify, implement and only relies on system structure. Furthermore, the theoretical results are applied to a typical fractional-order chaotic Hopfield neural network, and numerical simulation demonstrates the effectiveness and feasibility of the proposed method.

A new chaotic Hopfield neural network and its synthesis via parameter switchings

In this paper, we present a new chaotic attractor in Hopfield neural network. Numerical experiments show that the presented Hopfield neural network can display complex dynamics by changing the self-connection weight. Surprisingly, coexistence of a chaotic attractor and a limit cycle is found in this system, which means, the system can exhibit a chaotic attractor or a limit cycle according to different initial values, and this phenomenon is never reported before. We give a rigorous verification of existence of horseshoe chaos by virtue of topological horseshoes theory and estimates of topological entropy in the derived Poincaré maps. Finally, synthesis of the chaotic attractor is studied via parameter switching and a numerical example illustrates the effectiveness of this method.

Chaotic Hopfield Neural Network Swarm Optimization and Its Application

A new neural network based optimization algorithm is proposed. The presented model is a discrete-time, continuous-state Hopfield neural network and the states of the model are updated synchronously. The proposed algorithm combines the advantages of traditional PSO, chaos and Hopfield neural networks: particles learn from their own experience and the experiences of surrounding particles, their search behavior is ergodic, and convergence of the swarm is guaranteed. The effectiveness of the proposed approach is demonstrated using simulations and typical optimization problems.

Chaotic particle swarm optimization with neural network structure and its application

A new particle swarm optimization (PSO) algorithm having a chaotic Hopfield Neural Network (HNN) structure is proposed. Particles exhibit chaotic behaviour before converging to a stable fixed point which is determined by the best points found by the individual particles and the swarm. During the evolutionary process, the chaotic search expands the search space of individual particles. Using a chaotic system to determine particle weights helps the PSO to escape from the local extreme and find the global optimum. The algorithm is applied to some benchmark problems and a pressure vessel problem with nonlinear constraints. The results show that the proposed algorithm consistently outperforms rival algorithms by enhancing search efficiency and improving search quality.

Algebraic condition of synchronization for multiple time-delayed chaotic Hopfield neural networks

In this paper, an easy and efficient method is brought forward to design the feedback control for the synchronization of two multiple time-delayed chaotic Hopfield neural networks, whose activation functions and delayed activation functions can have different forms of mapping. Without many complex restrictions and Lyapunov analytic process, the feedback control is given based on the M-matrix theory, the system parameters and the feedback section coefficients. All the results are simulated by Matlab and Simulink, which shows the simplicity and validity of the control. As shown in the simulation results, the error systems converge to zero rapidly.

EMERGENT PERIODIC BEHAVIOR IN COUPLED CHAOTIC SYSTEMS

Emergent behavior in interconnected systems (complex systems) is of fundamental significance in natural and engineering sciences. A commonly investigated problem is how complicated dynamics take place in dynamical systems consisting of (often simple) subsystems. It is shown though numerical experiments that emergent order such as periodic behavior can likely take place in coupled chaotic dynamical systems. This is demonstrated for the particular case of coupled chaotic continuous time Hopfield neural networks. In particular, it is shown that when two chaotic Hopfield neural networks are coupled by simple sigmoid signals, periodic behavior can emerge as a consequence of this coupling.

Cryptography based on delayed chaotic neural networks

In this Letter, a novel approach of encryption based on chaotic Hopfield neural networks with time varying delay is proposed. We use the chaotic neural network to generate binary sequences which will be used for masking plaintext. The plaintext is masked by switching of chaotic neural network maps and permutation of generated binary sequences. Simulation results were given to show the feasibility and effectiveness in the proposed scheme of this Letter. As a result, chaotic cryptography becomes more practical in the secure transmission of large multi-media files over public data communication network.

Optimization of SF/sub 6/ circuit breaker based on chaotic neural network

The chaotic mechanism has been introduced to optimize the electric apparatus in this paper. By combining the chaotic mechanism and artificial neural network (ANN), the chaotic Hopfield neural network (CHNN) has been established, and applied to solve the optimum problem of the demonstrated examples. From the simulation results, it can be found that the proposed CHNN can be employed to solve the optimization problems with multivariables and complex energy function. Furthermore, a novel optimum algorithm for optimizing the electric apparatus has been provided

Chaos and transient chaos in simple Hopfield neural networks

In this paper a class of simple chaotic Hopfield neural networks is presented, and a bifurcation from transient chaos to chaos is discussed.

A Method to Combine Chaos and Neural Network Based on the Fixed Point Theory

The dynamics of either associative or hierarchical neural network can boil down to the discovery of fixed point or contraction to the already established fixed point in a discrete dynamical system, and strict mathematical calculations have already proven this point. In other words, the dynamics of all types of neural network can be analyzed and explained by using the fixed point theory in the traditional discrete dynamical system. What is equally important is that the explanation and classification of chaos can also be expressed in terms of its relationship with fixed points. This has provided an important link between chaos and neural network in the traditional discrete dynamical system, namely, the fixed point theory. Based on this idea, this paper proposes a method to combine chaos with neural network using the fixed point theory. With a view to practical application, the paper provides several examples on improving pattern recognition ability by adding chaotic noise in learning machines as well as on improving the ability of optimal solution in the large by creating a new Chaotic Hopfield Neural Network. The approach proposed by this paper is proved user friendly and universally applicable through lab experiments of pattern recognition and solution of the Traveling Salesman Problem on a set of 100 cities.