On Capacity with Incremental Learning by Simplified Chaotic Neural Network

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.

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.

Chaotic neural networks have been proved to be strong tools to solve the optimization problems. In order to escape the local minima, a new function is introduced into the self-feedback item of the transiently chaotic neural network, this paper proposes chaotic neural network with nonlinear function self-feedback by improving the self-feedback item of Chen and Aihara's network making that the network has new character which is different from linear self-feedback network. The figures of the reversed bifurcation and the maximal Lyapunov exponents of single neural unit were given, We constructed the energy function of chaotic neural network, and analyzed the sufficient condition for the networks to reach asymptotical stability and set the parameters of the networks for solving traveling salesman problem (TSP). The simulation results in solving 10-city TSP show that the new model is valid in solving optimization problems.

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

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.

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

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.

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.

Construction of blind restoration model for super-resolution image based on chaotic neural network

The chaotic neural network is studied under the threshold activated coupling, which provides a controlled output patterns. In general the chaotic neural network constructed with chaotic neurons exhibits very rich dynamic behaviors with a nonperiodic associative memory. In the chaotic neural network, it is difficult to distinguish the stored patterns from others, because of the chaotic states of output of the network. In order to apply the nonperiodic associative memory into information search and pattern recognition, etc, it is necessary to control chaos in this chaotic neural network. Chaos in the chaotic neural network is controlled with threshold activated coupling method and the network converges on one of its stored patterns or their reverses which has the smallest Hamming distance with the initial state of the network or provides a controlled neural network with spatio-temporal patterns depending upon the nature of control.

Studies Hebbian learning in linear neural networks with emphasis on the self-association information principle. This criterion, in one-layer networks, leads to the space of the principal components and can be generalized to arbitrary architectures. The self-association paradigm appears to be very promising because it accounts for the fundamental features of Hebbian synaptic learning and generalizes the various techniques proposed for adaptive principal component networks. The authors also include a set of simulations that compare various neural architectures and algorithms.

Chaotic recurrent neural networks and their application to speech recognition