A dimensional analysis 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.

In this paper, a new chaotic neural network model is proposed, we introduce a Bessel function as self-feedback term in this model, Compared with other chaotic neural network model, owing to the Bessel function is a nonlinear function with good nature, and it has stronger function approximation ability, so that the novel chaotic network model has stronger traversal search ability.When it is applied to solve combinatorial optimization problems, the simulation results show that the network has better ability to avoid network convergence to local minima if the appropriate coefficient of expansion and the network has been taken, so the efficiency of network optimization capability is improved.

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.

In the present study attempt has been made to obtain the dimensionality of atmosphere by using Grassberger and Proccacia's model of correlation dimension on pressure parameter for Ahmedabad station. Based on single variable time series, the dimension of pressure at tractor is evaluated to obtain a lower bound on the number of essential variables necessary to model atmospheric dynamics. A low dimensionality of the order of five to seven for the pressure variable was obtained if interannual and seasonal variabilities are excluded by using seasonal data.

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

Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays

This paper analyzes on the chaos characteristics of the chaotic neural networks and presents the convergence condition. Although the transient chaos of neural network sould be beneficial to overcome the local minimum problem and speed up the learning, the permanent chaotic response gives adverse effect on optimization problems and makes neural network unstable in general. This paper investigates the dynamic characteristics of the chaotic neural networks with the chaotic dynamic neuron, and presents the convergence condition for stabilizing the chaotic neural networks.

This paper proposes a new dynamical memory system based on chaotic neural networks, and its learning scheme. It is demonstrated that, when no embedded pattern, i.e., unknown pattern, is applied to the system, the output pattern travels around the embedded patterns, and the traveling phases depend on a external parameter of the networks such as the input from the other neurons or cortex. Further, the temporal output of the networks reflects a hierarchical structure of the memorized patterns.

This tutorial presents an in-depth introduction to chaos in dynamical systems, and presents several practical techniques for recognizing and classifying chaotic behavior. These techniques include the poincaré map, Lyapunov exponents, capacity, information dimension, correlation dimension, Lyapunov dimension, and the reconstruction of attractors from a single time series.

Coalmine gas explosion is unique to the extremely serious type of disaster. The root cause of gas explosion accident is the Overrun of the gas concentration. Gas concentration is forecast to achieve effective prevention of gas explosion accidents. According to the non-linear of gas concentration and the predictability of the chaotic time series, gas concentration phase space was reconstructed by the Takens theory. In the first, the time delay was attained by the mutual information method. Secondly the embedding dimension was determined by GP algorithm and the chaotic time series was predicted by the BP neural network. Finally, an example is given which shows the forecast results could approximate the actual situation well, and accomplishing the forecast objection of gas concentration.

Pattern recall in networks of chaotic neurons

1. In this study, neural network (NN) and response surface (RS) models were developed to investigate the response [average daily gain (ADG) and feed efficiency (FE)] of young broiler chickens to dietary protein and lysine. For this purpose, data on their responses to dietary protein and lysine were extracted from the literature and separate NN and RS models were constructed. 2. Comparison between the NN and RS models revealed higher accuracy of prediction with the NN models compared to the RS models. In terms of R 2 values, the NN models developed for both ADG (R 2 = 0.923) and FE (R 2 = 0.904) were far superior to the RS models (R 2 for ADG = 0.511; R 2 for FE = 0.67). This suggests that the NN models can serve as an alternative option to conventional regression approaches including use of RS models. 3. Optimisation of the NN models developed for response to protein and lysine showed that diets containing 220.7 (g/kg of diet) protein and 12.85 (g/kg of diet) lysine maximise ADG, whereas maximum FE is achieved with diets containing 241.3 and 13.12 (g/kg) protein and lysine, respectively. Based on the optimisation results, optimal dietary protein and lysine concentrations for maximum FE in broiler chickens during the starting period are higher than for ADG.

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

In a recent article, Chiarella [7] used a nonlinear supply curve with exactly one inflection point in the context of a cobweb model in order to make plausible that chaotic behaviour may result in such a model. There is, however, no exact proof under what conditions chaos can actually show up since Chiarella confines the analysis to a second order approximation to his difference equation. In a somewhat different model (a linear supply and a nonlinear demand curve which can be given a microeconomic foundation) we show that, under the formation of adaptive price expectations, the resulting adjustment mechanism can generate a wide range of dynamic behaviour (depending on the prevailing parameter constellations) such as stability, bifurcations with stable cycles of period 2, 4, 8, ... and, finally, aperiodic time paths, (i.e. we can show that period-3 cycles exist). In a second step, long historical time series of weekly price observations in German agricultural markets are scrutinized with regard to the hypothesis of nonlinearities. We study their correlation dimensions only recently employed by economists as a characteristic measure which allows, under certain conditions, to distinguish between deterministic chaos and random noise. Our results do not provide evidence to reject the hypothesis, although noise infection of the series cannot be ruled out.

Background: Data mining (DM) is an approach used in extracting valuable information from environmental processes. This research depicts a DM approach used in extracting some information from influent and effluent wastewater characteristic data of a waste stabilization pond (WSP) in Birjand, a city in Eastern Iran. Methods: Multiple regression (MR) and neural network (NN) models were examined using influent characteristics (pH, Biochemical oxygen demand [BOD 5 ], temperature, chemical oxygen demand [COD], total suspended solids [TSS], total dissolved solid [TDS], electrical conductivity [EC] and turbidity) as the regression input vectors. Models were adjusted to input attributes, effluent BOD 5 (BODout) and COD (CODout). The models performances were estimated by 10-fold external cross-validation. An internal 5-fold cross-validation was also used for the training data set in NN model. The models were compared using regression error characteristic (REC) plot and other statistical measures such as relative absolute error (RAE). Sensitivity analysis was also applied to extract useful knowledge from NN model. Results: NN models (with RAE = 78.71 ± 1.16 for BODout and 83.67 ± 1.35 for CODout) and MR models (with RAE = 84.40% ± 1.07 for BODout and 88.07 ± 0.80 for CODout) indicate different performances and the former was better (P < 0.05) for the prediction of both effluent BOD 5 and COD parameters. For the prediction of CODout the NN model with hidden layer size (H) = 4 and decay factor = 0.75 ± 0.03 presented the best predictive results. For BODout the H and decay factor were found to be 4 and 0.73 ± 0.03, respectively. TDS was found as the most descriptive influent wastewater characteristics for the prediction of the WSP performance. The REC plots confirmed the NN model performance superiority for both BOD and COD effluent prediction. Conclusion: Modeling the performance of WSP systems using NN models along with sensitivity analysis can offer better understanding on exploring the most significant parameters for the prediction of system performance. The findings of this study could build the foundation for prospective work on the characterization of WSP operations and optimization of their performances with a view to conducting statistical approaches.