Frequency conversion sinusoidal chaotic neural network and its application

In this paper, we examine the pattern separation ability in the Chaotic Quaternionic Associative Memory. The Chaotic Quaternionic Associative Memory is composed of chaotic quaternionic neuron model which is based on the chaotic neuron model and the quaternionic neuron model. If the parameters such as damping factor and scaling factor of refractoriness are set appropriately, the chaotic quaternionic neuron model can generate chaotic response. The Chaotic Quaternionic Associative Memory makes use of the dynamic association ability of the chaotic quaternionic neuron model in order to realize pattern separation. However, pattern separation ability is very sensitive to the parameters in chaotic quaternionic neuron model and the connection weight from external input. In this research, we examine the relation between pattern separation ability and the connection weight from external input in the Chaotic Quaternionic Associative Memory. We carried out a series of computer experiments and confirmed that the influence of the connection weight from external input to the pattern separation ability becomes large when the number of neurons increases.

For the phenomenon of premature occurred in the course of evolution of Hopfield neural network(HNN) and the slow convergence speed of Transient chaotic neural network(TCNN), a new blind detection algorithm based on composite sinusoidal chaotic neural network(CSCNN) is proposed in this paper. The presented algorithm experiences the process of coarse search based on chaos to fine search based on gradient dynamics characteristics and it can solve the blind detection of BPSK signal successfully taking advantages of the ergodic and stochastic characteristics of chaos. The simulation shows that: the novel algorithm not noly reduces the error rate dramaticlly but also increases the convergence rate tremendously of the algorithm.

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.

Pulse-type hardware chaotic neuron model and its bifurcation phenomena

This paper focuses on implementations of two modified Aihara's chaotic neuron models and a simple chaotic neural network constructed with two chaotic neurons in a programmable and reconfigurable manner with an analog programmable device, FPAA (Field Programmable Analog Array). After testing the chaotic behaviors of two chaotic neuron models and a simple chaotic neural network through numerical analyses that consist of time domain responses, phase portrait illustrations and bifurcation diagrams, the experimental setup is constructed with a FPAA device. The parametric adjustments of chaotic neural structures are possible with the proposed flexible design methodology and different chaotic neuron models are constructed on the same reconfigurable device without any hardware changes. Experimental results verify the dynamic behaviors of these chaotic neural structures and demonstrate the efficiency of programmable implementations.

A novel chaotic-neuron model is presented by introducing the non-monotonous activation function which is composed of the Legendre function and the Sigmoid function.The reversed bifurcation of the chaotic neuron model is given and analyzed, meanwhile, how do parameters influence the network convergence speed is discussed.Based on the neuron model, the piecewise simulated annealing SLF chaotic neural network was made by introducing the simulated annealing idea, the model improve the convergence speed, at the same time, the precision of this network have not being influenced.The simulation experiment of function optimization and TSP problem verify the effectiveness of the segmented simulated annealing strategy.

Chaotic simulated annealing by a neural network model with transient chaos

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.

This paper gives a general insight into how the neuron structure in a multilayer perceptron (MLP) can affect the ability of neurons to deal with classification. Most of the common neuron structures are based on monotonic activation functions and linear input mappings. In comparison, the proposed neuron structure utilizes a nonmonotonic activation function and/or a nonlinear input mapping to increase the power of a neuron. An MLP of these high power neurons usually requires a less number of hidden nodes than conventional MLP for solving classification problems. The fewer number of neurons is equivalent to the smaller number of network weights that must be optimally determined by a learning algorithm. The performance of learning algorithm is usually improved by reducing the number of weights, i.e., the dimension of the search space. This usually helps the learning algorithm to escape local optimums, and also, the convergence speed of the algorithm is increased regardless of which algorithm is used for learning. Several 2-dimensional examples are provided manually to visualize how the number of neurons can be reduced by choosing an appropriate neuron structure. Moreover, to show the efficiency of the proposed scheme in solving real-world classification problems, the Iris data classification problem is solved using an MLP whose neurons are equipped by nonmonotonic activation functions, and the result is compared with two well-known monotonic activation functions.

We report a study on learning ability of a deterministic Boltzmann machine (DBM) with neurons which have a nonmonotonic activation function. We use an end-cut-off-type function with a threshold parameter '/spl theta/' as the nonmonotonic function. Numerical simulations of nonlinear problems, such as the 2-parity problem and the 4-parity problem, show that the DBM network with nonmonotonic neurons has higher learning ability compared to the network with monotonic neurons.

Our goal is to investigate the piecewise linear difference equation xn+1 = βnxn – g(xn). This piecewise linear difference equation is a prototype of one neuron model with the internal decay rate β and the signal function g. The authors investigated this model with periodic internal decay rate βn as a period-two sequence. Our aim is to show that for certain values of coefficients βn, there exists an attracting interval for which the model is chaotic. On the other hand, if the initial value is chosen outside the mentioned attracting interval, then the solution of the difference equation either increases to positive infinity or decreases to negative infinity.

PDP networks that use nonmonotonic activation functions often produce hidden unit regularities that permit the internal structure of these networks to be interpreted (Berkeley et al., 1995; McCaughan, 1997; Dawson, 1998). In particular, when the responses of hidden units to a set of patterns are graphed using jittered density plots, these plots organize themselves into a set of discrete stripes or bands. In some cases, each band is associated with a local interpretation. On the basis of these observations, Berkeley (2000) has suggested that these bands are both subsymbolic and symbolic in nature, and has used the analysis of one network to support the claim that there are fewer differences between symbols and subsymbols than one might expect. We suggest below that this conclusion is premature. First, in many cases the local interpretation of each band is difficult to relate to the interpretation of a network's response; a more appropriate relationship only emerges when a band associated with one hidden unit is considered in the context of other bands associated with other hidden units (i.e., interpretations of distributed representations are more useful than interpretations of local representations). Second, the content that a band designates to an external observer (i.e., the interpretation assigned to a band by the researcher) can be quite different from the content that a band designates to the output units of the network itself.. We use two different network simulations – including the one described by Berkeley (2000) – to illustrate these points. We conclude that current evidence involving interpretations of nonmonotonic PDP networks actually illustrates the differences between symbolic and subsymbolic processing.

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.

This paper shows that the performance of the Hopfield network for solving optimization problems can be improved by using a new activation (output) function. The effects of the activation function on the performance of the Hopfield network are analyzed. It is shown that the sigmoid activation function in the Hopfield network is sensitive to noise of neurons. The reason is that the sigmoid function is most sensitive in the range where noise is most predominant. A new activation function that is more robust against noise is proposed. The new activation function has the capability of amplifying the signals between neurons while suppressing noise. The performance of the new activation function is evaluated through simulation. Compared with the sigmoid function, the new activation function reduces the error rate of tour length by 30.6% and increases the percentage of valid tours by 38.6% during simulation on 200 randomly generated city distributions of the 10-city traveling salesman problem.

This paper explores the multistability of S-asymptotically $\omega$-periodic solutions for fractional-order neural networks with time variable delays (FVDNNs). Benefited from the geometrical configuration of the nonlinear and non-monotonic activation function, we prove the coexistence of $(K+1)^{n}$ S-asymptotically $\omega$-periodic solutions with multiple asymptotical stability, where K is a positive integer. In contrast to the previous works, the obtained results extensively raise the amount of S-asymptotically $\omega$-periodic solutions of FVDNNs in this paper. Besides, two numerical examples are shown to illustrate the feasibility of obtained results.