A novel chaotic neural network with self-feedback

In this paper, anti-synchronization problem of two identical chaotic neural networks with time-varying delays is proposed. By using time-delay feedback control technique, mean value theorem and the Leibniz-Newton formula, and by constructing appropriately Lyapunov-Krasovskii functional, sufficient condition is proposed to guarantee the asymptotically anti-synchronization of two identical chaotic neural networks. This condition, which is expressed in terms of linear matrix inequality, rely on the connection matrix in the drive and response networks as well as the suitable designed feedback gains in the response network. Finally, the anti-synchronization of two chaotic cellular neural network and Hopfield neural network with time-varying delays are considered to illustrate the effectiveness of the proposed control scheme, in which, when compared with the nonlinear feedback control method, the proposed method shows superior performance. Key words: Lyapunov-Krasovskii functional, chaotic neural networks, anti-synchronization, time-varying delay, linear matrix inequality.

In this paper, the problem on sychronization is investigated for two different Chaotic Neural Network with mixed time-varying Delays. The adaptive synchronization of two different chaotic neural networks with fully unknown parameters and mixed time-varying delays is investigated, and as a result, a well-designed method is given to ensure the synchronization of two chaotic neural networks which are of the different structure and fully unknown parameters. Under the action of the adaptive control law, the synchronization and parametric identification can be done simultaneously. The controller designed is simple and easy to implement. Strict theoretical proofs are given by using the method of Lyapunov function. Finally, numerical simulations show the effectiveness of the method.

Design and investigation of a chaotic neural network architecture for cryptographic applications

Chaotic behaviors are often shown in the biological brains. They are related strongly to the memory storage and learning in the chaotic neural networks. The incremental learning is a method to compose an associative memory using a chaotic neural network and provides larger capacity than the Hebbian rule in compensation for amount of computation. In the former works, patterns were generated randomly to have plus 1 in half of elements and minus 1 in the others. When finely-tuned parameters were used, the network learned these pattern features, well. But, this result could be taken as an over-learning. Then, we proposed pattern generating methods to avoid over-learning and tested the patterns, in which the ratio of plus 1 and minus 1 is different from 1 to 1. In this paper, our simulations investigate the capacity of the usual chaotic neural network and that of the simplified chaotic neural network with these patterns to ensure no over-learning.

A Chaotic neural network model with Morlet wavelet function self-feedback is proposed by introducing Morlet wavelet function into self-feedback of chaotic neural network. The analyses of the optimization mechanism of the networks suggest that Morlet wavelet function self-feedback affects the original Hopfield energy function in the manner of the sum of the multiplications of Morlet wavelet function to the state, avoiding the network being trapped into the local minima. The energy function is constructed, and the sufficient condition for the networks to achieve asymptotical stability is analyzed and is used to instruct the parameter set of the networks for solving traveling salesman problem (TSP). Simulation researches on 10-city TSP indicate that the proposed networks can find the optimal solutions of combinatorial optimization problems.

Neural networks are able to learn more patterns with the incremental learning than with the correlative learning. The incremental learning is a method to compose an associate memory using a chaotic neural network. In former work, it was found that the capacity of the network increases along with its size, which is the number of the neurons in the network, until some threshold size and that it decreases over that size. The threshold size and the capacity varied between 2 different learning parameters. In this paper, the capacity of the networks was investigated changing the learning parameter. Through the computer simulations, it turned out that the capacity also increases in proportion to the network size in larger sizes and that the capacity of the network with the incremental learning is above 11 times larger than the one with correlative learning.

A novel image encryption/decryption scheme based on chaotic neural networks

We review our model of chaotic neural networks with chaotic dynamics and apply it to associative memory. We demonstrate that dynamical assocative memory can be realized with the chaotic neural network.

High quality clustering is impossible without a priori information about clustering criteria. The paper describes the development of new clustering technique based on chaotic neural networks that overcomes the indeterminacy about number and topology of clusters. Proposed method of weights computation via Delaunay triangulation allows to cut down computing complexity of chaotic neural network clustering.

In order to install a chaotic neural network to solve the traveling salesman problem (TSP) on an integrated circuit, a chaotic neuron circuit is designed by using a current mode circuit. First, the characteristics of the output function of the neuron circuit are determined by numerical simulation so that they have excellent capability to solve the TSP. Next, the network is designed such that the chaotic neural network consisting of the designed neuron circuits can seek the optimum solution efficiently. Further, a circuit is proposed which realizes chaotic annealing in order to improve the convergence of the chaotic neural network. The ability of the proposed network using the annealing circuit to derive an optimum solution of the TSP is studied. From the simulation results, it is confirmed that the proposed chaotic neuron circuit is suitable for integration of the chaotic neural network to solve the TSP. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(9): 52–62, 1999

This paper investigates the performance of current-mode chaotic neural networks that are optimized for travelling salesman problem (TSP). Piece-wise linear (PWL) functions used as the output functions in chaotic neurons are found to ease the design of neural network circuits. Three different PWL output functions are compared by solving 10-city TSP. Simulation results showed excellent performance of the chaotic neural networks with PWL output function. The design parameters to implement the PWL output function suitable for TSP chaotic neural networks are obtained.

The emergence of traveling waves is a universal property of nervous systems. However, mechanisms of these waves and their functional roles have not yet been fully elucidated. Here, we numerically investigate traveling waves in a locally connected large-scale chaotic neural network (CNN) consisting of more than one million units. We simulate it by parallel computing and visualize the network output by using color images. If the refractoriness of neurons is sufficiently large, many local cell assemblies are generated and the boundaries between them move as traveling waves. We also develop a simplified phenomenological model for the CNN by adding a negative self-feedback mechanism to the Potts model. The proposed meso-scopic model can qualitatively reproduce complex wave patterns in the CNN. Because the model requires less computational resources, it may serve as a useful tool for investigating traveling waves in nervous systems.

Traditional financial prediction models are difficult to cope with complex financial markets, especially cryptocurrency markets. In this paper, a quantum finance-based temporal chaotic neural oscillatory network (TSCNON) prediction model is used for the first time to predict the share price of Bitcoin by combining the quantum price level (QPL) technique with the theory of chaotic neural networks. Based on quantum field signalling (QFS) and Lee oscillator, the overfitting and deadlocking problems of traditional neural networks when dealing with large-scale financial data are solved. The structural design of the TSCNON model and its training algorithm are presented. The application framework of TSCNON in Bitcoin price prediction is demonstrated. Experimental results show that the TSCNON model can greatly reduce the prediction error and improve the prediction accuracy. This paper provides financial market participants with more accurate and reliable prediction tools and promotes the promotion of quantum financial technology in practical applications.

The global shift towards digitization has resulted in intensive research on Cryptographic techniques. Chaotic neural networks, augment the process of cryptography by providing increased security. In this paper, a description of an algorithm for the generation of an initial value for encryption using neural network involving memristor and chaotic polynomials is provided. The chaotic series that is obtained is combined with nonlinear 1 Dimensional and 2 Dimensional chaotic equations for the encryption process. A detailed analysis is performed to find the fastest converging neural network, complemented by the chaotic equations to produce least correlated ciphertext and plaintext. The use of Memristor in Neural Network as a generator for chaotic initial value as the encryption key and the involvement of nonlinear equations for encryption, makes the communication more confidential. The network can further be used for secure multi receiver systems.

With the macroeconomy entering a new normal, many new problems are exposed in all walks of life, and the risk of default in the financial sector is also being exposed at an accelerated pace. In the context of big data, internet finance, as an important part of the financial market, also faces many risks in the process of its rapid development. Reasonable, scientific, and effective prediction and prevention of financial default risk have become a key link in the process of risk management practice in the financial industry. Based on the powerful prediction function of the neural network, this paper combined neural network and chaos theory to construct a chaotic RBF neural network. It was applied to financial default risk prediction, which made the prediction accuracy and efficiency higher. The chaotic neural network solves the shortcomings of unstable prediction in the basic neural network and can comprehensively and accurately predict the financial default risk, so as to take measures to prevent risks. The experimental results of this paper show that the accuracy rate of the chaotic RBF neural network reaches 95%, while the accuracy rates of the BP neural network and the RBF neural network are 67% and 78%, respectively. Although the prediction accuracy of these two methods is also high, it is still not as high as the chaotic RBF neural network. Therefore, it is very meaningful to choose the chaotic RBF neural network to predict financial default risk in this paper.