Blind detection algorithm based on composite sinusoidal chaotic neural network

The optimization performance of transiently chaotic neural network (TCNN) is affected by various factors such as chaotic characteristic, model parameters, and annealing function, and its capacity of global optimization is limited. It is demonstrated that the non-monotonic activation function can generate richer chaotic characteristic than the monotonic activation function in the TCNN model. Besides, the activation function involving neurobiological mechanism can not only reflect the rich brain activity in brain waves, but also enhance the non-linear dynamic characteristic, which may further improve the global optimization ability. Hence, a novel chaotic neuron model is proposed with the non-monotonic activation function based on the neurobiological mechanisms from the electroencephalogram. The electroencephalogram consists of five brain waves (i.e., , , , , and waves) which are defined by the quality and intensity of brain waves with different frequency bands ranging from 0.5 Hz to 100 Hz. The brain wave with a higher frequency and a lower amplitude represents a more active brain. Researches demonstrate that the five brain waves can be simplified into sinusoidal waves with different frequencies. Hence, a frequency conversion sinusoidal (FCS) function which has the consistent frequency range and features with brain waves is designed based on the above neurobiological mechanisms. Then a novel chaotic neuron model with non-monotonic activation function which is composed of the FCS function and sigmoid function, is proposed for richer chaotic dynamic characteristic. The reversed bifurcation and the Lyapunov exponent of the chaotic neuron are given and the dynamic system is analyzed, indicating that the proposed FCS neuron model owns richer chaotic dynamic characteristic than transiently chaotic neuron model due to its special non-monotonic activation function. Based on the neuron model, a novel transiently-chaotic neural networkfrequency conversion sinusoidal chaotic neural network (FCSCNN) is constructed and the basis of model parameter selection is provided as well. To validate the effectiveness of the proposed model, the FCSCNN is applied to nonlinear function optimization and 10-city, 30-city, 75-city traveling salesman problem. The experimental results show that 1) the FCSCNN has a good performance under the condition of moderate a, smaller cA(0) and 2(0); 2) on the basis of the appropriate model parameters, the FCSCNN has better global optimization ability and optimization accuracy than Hopfield neural network, TCNN, improved-TCNN due to its richer chaotic characteristic in complicated combinational optimization problem, especially in middle and large scale problem.

A novel approach using transient chaotic neural network (TCNN) and self-organizing feature map (SOFM) process to solve large-scale combinatorial optimization problems has been proposed. With the clustering function of self-organizing feature map, the computational cost of a large-scale combinatorial optimization problem solved by TCNN is reduced. Numerical simulation of TSP shows that the proposed method is effective to solve large-scale optimization problems.

Chaotic simulated annealing by a neural network model with transient chaos

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.

Current E-commerce technologies cannot provide enough individual information to buyers. Augmented Reality (AR) technology might improve the performance of E-commerce by overlaying virtual information of products on the real world. But usual tracking technology based on markers is impeding the application of AR technology in business. This paper proposes an approach to feature point correspondence of image sequence based on transient chaotic neural networks. Through this approach a new markerless visual tracking technology with image feature can be used in AR E-commerce applications. Feature point based neural network image matching method has attracted considerable attention in recent years. Rotation and scale invariant features are extracted from images firstly, and then transient chaotic neural network is used to perform global feature matching and perform the initialization phase of the tracking. Experimental results demonstrate the efficiency and the effectiveness of the proposed method.

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.

The paper proposes a new method to blindly detect QPSK signals of MIMO systems by using continuous Hopfield neural network (HNN). The new method successfully constructs a weighted matrix of HNN, which reduces the number of equilibrium points of HNN significantly, so that the speed to blindly detect signals is increased as well as the bit error rate (BER) is lowered. The new method detects multi-user signals with serial processing, in which the method utilizes those user signal vectors having been detected to extend the complementary subspace consisting of received data vectors in order to recover other user signals to be detected. The performance of the proposed HNN-based method is evaluated via computer simulations and compared with the existing approaches. Results are shown that the new method has better performances than others.

In 1984 Hopfield showed that the time evolution of a symmetric Hopfield neural networks are a motion in state space that seeks out minima in the energy function (i.e., equilibrium point set of Hopfield neural networks). Because high-order Hopfield neural networks have more extensive applications than Hopfield neural networks, and have been discussed on the convergence of the networks. In practice, a neural network is often subject to environmental noise. It is therefore useful and interesting to find out whether the high-order neural network system still approacher some limit set under stochastic perturbation. In this paper, we will give a number of useful bounds for the noise intensity under which the stochastic high-order neural network will approach its limit set. Our result cancels the requirement of symmetry of the connection weight matrix and includes the classic result on Hopfield neural networks, which is a special case of stochastic high-order Hopfield neural networks. In the end, A example is given to verify the effective of our results.

In this paper, an automatic determination algorithm for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations is presented. In such method, the problem of NMR spectrum determination is transformed into the determination of the parameters of a mathematical model of the NMR signal. To calculate these parameters efficiently, a new model called Hopfield neural network is designed. The main achievement of this paper over the work in literature [30] is that the speed of the Hopfield neural network is accelerated. This is done by applying cross correlation in the frequency domain between the input values and the input weights. The Hopfield neural network can accomplish complex dignals perfectly with out any additinal computation steps. This is a valuable advantage as NMR signals are complex-valued. In addition, a technique called modified sequential extension of section (MSES) that takes into account the damping rate of the NMR signal is developed to be faster than that presented in [30]. Simulation results show that the calculation precision of the spectrum improves when MSES is used along with the neural network. Furthermore, MSES is found to reduce the local minimum problem in Hopfield neural networks. Moreover, the performance of the proposed method is evaluated and there is no effect on the performance of calculations when using the Hopfield neural networks.

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.

At present, the blind detection of DSSS (direct sequence spread spectrum) signals is mainly based on the cyclostationarity of the signals and uses the statistics analysis of the second or higher order eigenvalues as a cut-in sticking point for resolving the problem, it is quite easily influenced by the low signal to noise ratio and restricted by the implementation of the algorithm. In order to resolve the problem of the blind detection, the paper proposes a blind spread spectrum pseudo random sequence detection method: multi-chip allied correlation detection, and a blind chip synchronization method: multi-codeword correlation smoothing match. The proposals of the paper resolve the bottleneck problems in the blind detection of DSSS signals: the blind spread spectrum pseudo random sequence estimation and the chip synchronization search in the context of low signal to noise ratio. The proposed methods not only avoid the need of the second or higher order processing of many blind detection methods, reduce the complexity of the blind detection of DSSS signals greatly, but also overcome the shortcoming of many blind detection methods while dealing with the spread spectrum transmission far below the noise level. The paper may be a foundation for achieving the detection of the DSSS signals in non-cooperative context.

For the blindness in initialization of particle swarm optimization algorithm and the phenomenon of premature occurred in the course of evolution, a new algorithm is proposed in this paper: blind detection algorithm based on adaptive chaotic particle swarm optimization. The performance simulation shows that, using of randomness and ergodicity of chaos, the improved algorithm compared with the method in the literature has more advantages like good global convergence, fast convergence speed and low bit error rate. This new algorithm can solve blind detection problem successfully.

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

Information processing and two types of memory in an analog neural network model with time delay that produces chaos similar to the human and animal EEGs are considered. There are two levels of information processing in this neural network: the level of individual neurons and the level of the neural network. Similar to the state of brain, the state of chaotic neural network is defined. It is characterized by two types of memories (memory I and memory II) and correlation structure between the neurons. In normal (unperturbed) state, the neural network generates chaotic patterns of averaged neuronal activities (memory I) and patterns of oscillation amplitudes (memory II). In the presence of external stimulation, the activity patterns change, showing changes in both types of memory. As in experiments on stimulation of the brain, the neural network model shows synchronization of neuronal activities due to stimulus measured by Pearson's correlation coefficient. An increase in neural network asymmetry (increase of the neural network excitability) leads to the phenomenon similar to the epilepsy. Modeling of brain injury, Parkinson's disease, and dementia is performed by removing and weakening interneuron connections. In all cases, the chaotic neural network shows a decrease of the degree of chaos and changes in both types of memory similar to those observed in experiments with healthy human subjects and patients with Parkinson's disease and dementia. © 2005 Wiley Periodicals, Inc. Complexity 11:39–52, 2005

Improvement and Application of Transient Chaos Neural Networks