An Improved Delay Feedback Control Method in a Chaotic Neural Network

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.

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.

Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.

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

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

In this paper, we propose a chaotic neural network with time delay term (CNNTD). The proposed model is based on the conventional chaotic neural network and has two types of connection weights; (1) normal weights for hetero associations and (2) weights with time delay for auto associations. In the proposed model, dynamic associations between patterns belong to the same group in short term and dynamic associations between groups in long term are realized. We carried out a series of computer experiments and confirmed that the effectiveness of the proposed model.

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.

This paper proposes a model of fuzzy chaotic neuron (FCN), which is derived from chaotic neuron, as to combine fuzzy logic with chaotic neural network. We first give the expression of FCN and analyze its fuzzy character, scattering character and Lyapunov exponent separately. Some restrains of the parameter k are deduced to make sure the FCN has both fuzzy and chaotic character. After that the paper constructs a fuzzy chaotic neural network (FCNN) on the basis of FCN, and list weight-updating method. At last is an example, in which a fuzzy self-associate problem is solved using FCNN.

A new transient chaotic neuron model which introduces Legendre function into the self-feedback term is constructed. The dynamic characteristics of the single neuron are analyzed by the time evolution graph and the inverted bifurcation graph of the largest Lyapunov exponent. The network parameters are set for settling the combinatorial optimization problem. The effectiveness of this model has been verified by the simulation results in nonlinear function optimization, traveling salesman problem (TSP).KeywordsChaotic neural networkLegendre function self-feedbackLyapunov exponentsCombinatorial optimization problem

In this paper, we propose a knowledge processing system using chaotic associative memory (KPCAM). KPCAM is based on a chaotic neural network (CAM) composed of chaotic neurons. In conventional chaotic neural network, when a stored pattern is given continuously to the network as an external input, the input pattern vicinity is searched. The CAM makes use of this property to separate superimposed patterns and to deal with many-tomany associations. In this research, the CAM is applied to knowledge processing in which knowledge is represented in a form of semantic network. The proposed KPCAM has the following features: (1) it can deal with knowledge represented in a form of semantic network; (2) it can deal with characteristic inheritance; (3) it is robust for noisy input. A series of computer simulations shows the effectiveness of the proposed system.

Direct-current (DC) bus systems are expected to play a significant role in next-generation power technology because of the rapid development of power electronics. However, it is well known that the bus line voltage can become unstable when electric power through the bus line is constantly consumed by loads. Bifurcation analysis of this instability has been previously performed. It has been reported that in theory, delayed feedback control, which was developed to stabilize chaotic systems, can suppress this instability. For practical applications, it is necessary to confirm these analytical results with circuit experiments. In this study, the dynamics of a DC bus system without control and with delayed feedback control are experimentally investigated. The following three main results are obtained. First, bifurcation phenomena are experimentally found to occur with an increase in power consumption in the DC bus system without control. Second, it is experimentally found that delayed feedback control stabilizes the operating point. These results provide experimental evidence that delayed feedback control can be utilized as a stabilization method for DC bus systems. Third, it is experimentally demonstrated that the delayed feedback controller can track the operating point when the power consumption changes slowly, but not when it changes rapidly. A frequency-domain analysis is conducted to analytically estimate the upper limit of the acceptable power consumption rate of change. The estimated upper limit is useful for designing the controller and restricting the change rate of power consumption.

The Seventh International Symposium on Neural Networks (ISNN 2010) was held on June 6–9, 2010 in Shanghai, China. The ISNN 2010 was a great success and provided a high-level international forum for scientists and engineers to present the latest research in neural networks, computational intelligence, cognitive systems, and related fields. To highlight the success of this conference, we edited this special issue for Cognitive Computation. We chose nine papers from over 591 papers submitted to ISNN 2010, which reflect the high quality of the presentations at the conference while capturing the spirit of our theme, ‘‘Advances in Computational Intelligence and Applications,’’ for this special issue. Our goal for this special issue is to present the latest research developments in computational intelligence with a focus on cognitive computation and their applications across a wide range of domains. Over the past decades, we have witnessed tremendous interest and developments in all aspects of computational intelligence research, ranging from both theoretical foundations, principles, to practical applications in different domains. To reflect a flavor of recent research activities in the community, we carefully selected these nine papers for this special issue. The selected papers can be organized into the following four coherent sections. The first section is directly related to neural network models and applications. The paper by Deng presents a new control strategy for the chaotic neural network, in which the refractoriness is tuned by using feedback control based on online averaging of network states. Simulation results demonstrate that the proposed model can achieve favorable performance in handling noisy, incomplete, and composite patterns, while also achieving either enhanced or comparable memory capacity compared with the classic Hopfield net and other chaotic neural network models. In the other paper, Gluge et al. discuss recurrent networks for implicit learning of temporal sequences, a very important area to understand high-level cognitive intelligence. The authors propose a recurrent network with backpropagation training algorithm that is adapted to the reinforcement learning scheme. The simulation results fit quantitatively as well as qualitatively to the behavioral results, suggesting the role of temporal context in associative learning scenarios. The second section is related to language processing and understanding, an important topic in cognitive science and computational intelligence. The paper by Murata et al. investigates the maximum entropy (ME) approach for natural language processing (NLP) problems including machine translation and information extraction. Comparative studies of the proposed approach with the existing techniques are illustrated in this paper. In related work to this field, the paper by Kaznatcheev investigates connectionist models on the interplay of nouns and pronouns in personal pronoun acquisition, a very interesting and important problem in psychology. For instance, the author discusses the learning in the shifting reference situation for children. It is reported that learning of two different noun-and-pronoun addressee patterns is consistent with Z. Zeng (&) Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China e-mail: zgzeng@gmail.com

Comparison of the Kriging and neural network methods for modeling foF2 maps over North China region

In the last few decades, the stabilization in stationary states has emerged as a new auspicious campaigner in chaos theory and found a celebrated place through various control techniques such as predictive control, delayed feedback control, constant proportional feedback control and oscillating feedback control system. Generally, it is accepted that the superiority of control systems is not only to quash the irregular distribution of stationary states, but also to illustrate its basin of attractions as large as possible depending on the numerical as well as analytical observance. In this article, the universal stabilization in unstable stationary states is studied through superior fixed point feedback control system for a family of one-dimensional maps. Further, it is interesting to know that the novel system provides freedom in the control parameter γ due to which the stabilization increases more rapidly for the lager range of parameter γ in [0,1]. The analytical as well as numerical simulations are demonstrated to examine the behavior of parameter γ for which the unstable stationary state admits universal stability.

The synchronisation problem of Lorenz system is further investigated in this paper. On the basis of the Lyapunov stability theory, some simple and useful criteria for synchronisation to be delay-independent asymptotically stable are presented via combining drive and Delayed Feedback Control (DFC) methods. Especially, only one controller is needed to obtain synchronisation asymptotically. Theoretical analysis and numerical simulations show the effectiveness and feasibility of the proposed schemes.