Bessel Function Self-Feedback Chaotic Neural Network Model and Applications

We apply a dimensional analysis to a neural network model with chaotic dynamics, or a mathematical model of chaotic neural networks. First, Lyapunov spectra are examined to confirm existence of chaotic network behavior and to calculate the Lyapunov dimension. Then, the correlation dimension is estimated in the following three cases: (1) reconstruction from single variable time series, (2) observation in state subspaces and (3) observation of the macroscopic average activity. The results show good correlation dimension obtained by observation in state subspaces and the characteristics of the correlation dimension estimated by macroscopic observation.

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

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 Chaotic neural network model with Morlet wavelet function self-feedback is proposed by introducing Morlet wavelet function into self-feedback of chaotic neural network. The analyses of the optimization mechanism of the networks suggest that Morlet wavelet function self-feedback affects the original Hopfield energy function in the manner of the sum of the multiplications of Morlet wavelet function to the state, avoiding the network being trapped into the local minima. The energy function is constructed, and the sufficient condition for the networks to achieve asymptotical stability is analyzed and is used to instruct the parameter set of the networks for solving traveling salesman problem (TSP). Simulation researches on 10-city TSP indicate that the proposed networks can find the optimal solutions of combinatorial optimization problems.

The present study examines the possible roles of cortical chaos in generating novel actions for achieving specified goals. The proposed neural network model consists of a sensory-forward model responsible for parietal lobe functions, a chaotic network model for premotor functions and prefrontal cortex model responsible for manipulating the initial state of the chaotic network. Experiments using humanoid robot were performed with the model and showed that the action plans for satisfying specific novel goals can be generated by diversely modulating and combining prior-learned behavioral patterns at critical dynamical states. Although this criticality resulted in fragile goal achievements in the physical environment of the robot, the reinforcement of the successful trials was able to provide a substantial gain with respect to the robustness. The discussion leads to the hypothesis that the consolidation of numerous sensory-motor experiences into the memory, meditating diverse imagery in the memory by cortical chaos, and repeated enaction and reinforcement of newly generated effective trials are indispensable for realizing an open-ended development of cognitive behaviors.

Effects of correlation among stored patterns on associative dynamics of chaotic neural network

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.

Pattern recall in networks of chaotic neurons

S-box (Substitution box) is one of the most important components in the block cipher. In this paper, the main indices to evaluate S-box are firstly introduced. Then an algorithm for obtaining cryptographical strong S-boxes based on chaotic neural network is proposed. The chaotic neural network used to design S-boxes is composed of two layers, which have sixteen and eight neurons, respectively. Owing to making full use of the nonlinearity of the chaotic network, some S-boxes with good cryptographical performance can be produced. Therefore, the proposed method is a promising choice for designing S-boxes and suitable for designing block cryptosystem with dynamical S-boxes.

Exploring microstructure evolution and machine-learning methods based on SCAT-CIWOA-BP-DMM theory during hot deformation of 56Ni–32Ti–12Hf alloy

Through adding a nonlinear self-feedback term in the evolution equations of neural network, we introduced a transiently chaotic neural network model. In order to utilize the transiently chaotic dynamics mechanism in optimization problem efficiently, we have analyzed the dynamical procedure of the transiently chaotic neural network model and studied the function of the crucial bifurcation parameter which governs the chaotic behavior of the system. Based on the dynamical analysis of the transiently chaotic neural network model, chaotic annealing algorithm is also examined and improved. As an example, we applied chaotic annealing method to the traveling salesman problem and obtained good results.

A new chaotic network model for epilepsy

The new approach for combinatorial optimization problems using chaotic dynamics is discussed. We show effectiveness of chaotic neuro dynamics for solving combinatorial optimization problems by applying the chaotic neural network to traveling salesman problems. In this paper, we adopt the chaotic neural network model with two internal states, corresponding to mutual interactions which minimize an energy function and refractoriness which induce chaotic dynamics. We investigate relationships between solving abilities and different model parameters such as decay parameters of two internal states, Lyapunov exponents and first order statistics of firing patterns.

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.

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