Shigetoshi Nara

CHAOTIC MEMORY DYNAMICS IN A RECURRENT NEURAL NETWORK WITH CYCLE MEMORIES EMBEDDED BY PSEUDO-INVERSE METHOD

It is shown that hierarchical bifurcation of chaotic intermittency among memories can be induced by reducing neural connectivity when sequences of similar patterns are stored in a recurrent neural network using the pseudo-inverse method. This chaos is potentially useful for memory search and synthesis.

Completely reproducible description of digital sound data with cellular automata

Abstract A novel method of compressive and completely reproducible description of digital sound data by means of rule dynamics of CA (cellular automata) is proposed. The digital data of spoken words and music recorded with the standard format of a compact disk are reproduced completely by this method with use of only two rules in a one-dimensional CA without loss of information.

A solution for two-dimensional mazes with use of chaotic dynamics in a recurrent neural network model

Chaotic dynamics introduced into a neural network model is applied to solving two-dimensional mazes, which are ill-posed problems. A moving object moves from the position at t to t + 1 by simply defined motion function calculated from firing patterns of the neural network model at each time step t. We have embedded several prototype attractors that correspond to the simple motion of the object orienting toward several directions in two-dimensional space in our neural network model. Introducing chaotic dynamics into the network gives outputs sampled from intermediate state points between embedded attractors in a state space, and these dynamics enable the object to move in various directions. System parameter switching between a chaotic and an attractor regime in the state space of the neural network enables the object to move to a set target in a two-dimensional maze. Results of computer simulations show that the success rate for this method over 300 trials is higher than that of random walk. To investigate why the proposed method gives better performance, we calculate and discuss statistical data with respect to dynamical structure.

Yukawa system (dusty plasma) in one-dimensional external fields

Abstract The behavior of the Yukawa system in external one-dimensional force fields is analyzed by molecular dynamics simulation. The formation of layered structures at low temperatures is observed and the relation between the number of layers and characteristic parameters of the system is obtained. Periodic boundary conditions are imposed in two dimensions and deformations of periodic boundaries are allowed in order to reduce the effect of boundaries without placing too much constraint on the symmetry.

SENSITIVE RESPONSE OF A CHAOTIC WANDERING STATE TO MEMORY FRAGMENT INPUTS IN A CHAOTIC NEURAL NETWORK MODEL

Dynamical properties of a chaotic neural network model in a chaotically wandering state are studied with respect to sensitivity to weak input of a memory fragment. In certain parameter regions, the network shows weakly chaotic wandering, which means that the orbits of network dynamics in the state space are localized around several memory patterns. In the other parameter regions, the network shows highly developed chaotic wandering, that is, the orbits become itinerant through ruins of all the memory patterns. In the latter case, once the external input consisting of a memory fragment is applied to the network, the orbit quickly moves to the vicinity of the corresponding memory pattern including the memory fragment within several iteration steps. Thus, chaotic dynamics in the model is effective for instantaneous search among memory patterns.

RESPONSE PROPERTIES OF A SINGLE CHAOTIC NEURON TO STOCHASTIC INPUTS

Response properties of a single chaotic neuron to stochastic inputs are investigated by means of numerical simulations in the context of a nonlinear dynamical approach to analyzing chaotic behaviors of a neuron. We apply six kinds of stochastic inputs with the same mean rate but different correlations of interspike intervals, whose timings are determined by a stochastic process, namely, Markovian processes and Gaussian/Poisson random processes. From numerical evaluations of entropy and conditional entropies with respect to interspike intervals of outputs, it is shown that interspike intervals of outputs represent dynamical structures of each input. Numerical calculations of Lyapunov exponents, trajectories of dynamics and return plots of internal states make meaningful difference in dynamical properties of the model depending on inputs even if mean interspike intervals of outputs are almost the same values. In order to extract dynamical features of outputs, we calculate a time-delayed space representation of output responses to inputs, and the results provide different trajectories in a time-delayed phase space, which reflect a higher order statistical feature of inputs, amplifying their feature differences. For signals containing noise, the behaviors of the model do not suffer degradation, showing robustness to noise in the inputs. As conclusion, our results show that dynamical properties of inputs can be extracted with clear difference of response properties of the model, that is, the model gives a variety of the amplitude and the interspike intervals of outputs depending on inputs. In other words, the model can realize dynamical sampling of inputs with sensitivity of response properties to inputs and robustness to inputs with noise.

Dynamical Responses of Chaotic Memory Dynamics to Weak Input in a Recurrent Neural Network Model

Chaotic dynamics in a recurrent neural network model, in which limit cycle memory attractors are stored, is investigated by means of numerical methods. In particular, we focus on quick and sensitive response characteristics of chaotic memory dynamics to external input, which consists of part of an embedded memory attractor. We have calculated the correlation functions between the firing activities of neurons to understand the dynamical mechanisms of rapid responses. The results of the latter calculation show that quite strong correlations occur very quickly between almost all neurons within 1 ~ 2 updating steps after applying a partial input. They suggest that the existence of dynamical correlations or, in other words, transient correlations in chaos, play a very important role in quick and/or sensitive responses.

Chaotic neural network applied to two-dimensional motion 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.

Application of chaotic dynamics in a recurrent neural network to control: hardware implementation into a novel autonomous roving robot

Originating from a viewpoint that complex/chaotic dynamics would play an important role in biological system including brains, chaotic dynamics introduced in a recurrent neural network was applied to control. The results of computer experiment was successfully implemented into a novel autonomous roving robot, which can only catch rough target information with uncertainty by a few sensors. It was employed to solve practical two-dimensional mazes using adaptive neural dynamics generated by the recurrent neural network in which four prototype simple motions are embedded. Adaptive switching of a system parameter in the neural network results in stationary motion or chaotic motion depending on dynamical situations. The results of hardware implementation and practical experiment using it show that, in given two-dimensional mazes, the robot can successfully avoid obstacles and reach the target. Therefore, we believe that chaotic dynamics has novel potential capability in controlling, and could be utilized to practical engineering application.

Simultaneous multichannel signal transfers via chaos in a recurrent neural network

We propose neural network model that demonstrates the phenomenon of signal transfer between separated neuron groups via other chaotic neurons that show no apparent correlations with the input signal. The model is a recurrent neural network in which it is supposed that synchronous behavior between small groups of input and output neurons has been learned as fragments of high-dimensional memory patterns, and depletion of neural connections results in chaotic wandering dynamics. Computer experiments show that when a strong oscillatory signal is applied to an input group in the chaotic regime, the signal is successfully transferred to the corresponding output group, although no correlation is observed between the input signal and the intermediary neurons. Signal transfer is also observed when multiple signals are applied simultaneously to separate input groups belonging to different memory attractors. In this sense simultaneous multichannel communications are realized, and the chaotic neural dynamics acts as a signal transfer medium in which the signal appears to be hidden.