Tohru Ikeguchi

Associative dynamics in chaotic neural networks

The authors apply a model of a chaotic neural network composed of neuron models with chaotic dynamics to associative memory, the stored patterns of which are mutually orthogonal, and analyze its dynamical behavior quantitatively. In order to clarify the chaotic dynamics, they calculate the Lyapunov spectrum, the temporal changes of the distance between the output pattern of the chaotic neural network and the stored patterns, and the local divergence rate. It is demonstrated that dynamical associative memory can be realized with the chaotic neural network.<<ETX>>

A novel chaotic search for quadratic assignment problems

Abstract We propose a novel method for solving the quadratic assignment problems. First, we realize the conventional tabu search on a neural network, and modify it to a chaotic version. Our novel method includes both effects of chaotic dynamics and tabu search. We compare the performance of the novel chaotic search with the conventional tabu search and an exponential tabu search whose memory effect for tabu (forbidding previous moves) decays exponentially. We show that the exponential tabu search has higher performance than the conventional tabu search, and further that the novel method with a chaotic neural network exhibits the best performance. We also propose a controlling method of the chaotic neural network for realizing easy and robust applications of our method. Then, better performance can be realized without manual parameter setting for various problems.

Solving large scale traveling salesman problems by chaotic neurodynamics

We propose a novel approach for solving large scale traveling salesman problems (TSPs) by chaotic dynamics. First, we realize the tabu search on a neural network, by utilizing the refractory effects as the tabu effects. Then, we extend it to a chaotic neural network version. We propose two types of chaotic searching methods, which are based on two different tabu searches. While the first one requires neurons of the order of n2 for an n-city TSP, the second one requires only n neurons. Moreover, an automatic parameter tuning method of our chaotic neural network is presented for easy application to various problems. Last, we show that our method with n neurons is applicable to large TSPs such as an 85,900-city problem and exhibits better performance than the conventional stochastic searches and the tabu searches.

Deterministic prediction and chaos in squid axon response

Abstract We make deterministic predictive models of apparently complex squid axon response to periodic stimuli. The result provides evidence that the response is chaotic (and therefore partially predictable) and implies the possibility of identifying deterministic chaos in other kinds of noisy data even when explicit models are not available.

Stdp provides the substrate for igniting synfire chains by spatiotemporal input patterns

Spike-timing-dependent synaptic plasticity (STDP), which depends on the temporal difference between pre- and postsynaptic action potentials, is observed in the cortices and hippocampus. Although several theoretical and experimental studies have revealed its fundamental aspects, its functional role remains unclear. To examine how an input spatiotemporal spike pattern is altered by STDP, we observed the output spike patterns of a spiking neural network model with an asymmetrical STDP rule when the input spatiotemporal pattern is repeatedly applied. The spiking neural network comprises excitatory and inhibitory neurons that exhibit local interactions. Numerical experiments show that the spiking neural network generates a single global synchrony whose relative timing depends on the input spatiotemporal pattern and the neural network structure. This result implies that the spiking neural network learns the transformation from spatiotemporal to temporal information. In the literature, the origin of the synfire chain has not been sufficiently focused on. Our results indicate that spiking neural networks with STDP can ignite synfire chains in the cortices.

2005 Special issue: A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems

We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.

Solving combinatorial optimization problems by nonlinear neural dynamics

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.

Analysis of Chaotic Dynamics Using Measures of the Complex Network Theory

Complex phenomena are observed in various situations. These complex phenomena are produced from deterministic dynamical systems or stochastic systems. Then, it is an important issue to clarify what is a source of the complex phenomena and to analyze what kind of response will emerge. Then, in this paper, we analyze deterministic chaos from a new aspect. The analysis method is based on the idea that attractors of nonlinear dynamical systems and networks are characterized by a two-dimensional matrix: a recurrence plot and an adjacent matrix. Then, we transformed the attractors to the networks, and evaluated the clustering coefficients and the characteristic path length to the networks. As a result, the networks constructed from the chaotic systems show a small world property.

Estimating Correlation Dimensions of Biological Time Series with a Reliable Method

This article deals with a problem on estimating correlation dimensions of possible attractors reconstructed from biological time series data. The analyzed data are the five Japanese vowels, /a/, /i/, /u/, /e/, and /o/, and two pulse waves in human finger capillary vessels. The estimation algorithm used here is not the conventional Grassberger-Procaccia algorithm, but a new method proposed by Judd, which solves some problems intrinsic to the conventional method. To avoid several artifacts that might be involved in the analysis, such as the limited number of time series data, the finite resolution of data points, and the existence of the observational noise, the statistical procedure or the method of surrogate data is also applied to the real data. As a result, the existence of strange attractors with fractional dimensions are implied in the Japanese vowels /a/ and /o/. Although nonlinearities in the Japanese vowels /i/, /u/, and /e/, and pulse waves in human capillary vessels are implied by the analysis with the method of surrogate data, we cannot conclude that these data have definite fractal structures.

Colored noise induces synchronization of limit cycle oscillators

Driven by various kinds of noise, ensembles of limit cycle oscillators can synchronize. In this letter, we propose a general formulation of synchronization of the oscillator ensembles driven by common colored noise with an arbitrary power spectrum. To explore statistical properties of such colored noise-induced synchronization, we derive the stationary distribution of the phase difference between two oscillators in the ensemble. This analytical result theoretically predicts various synchronized and clustered states induced by colored noise and also clarifies that these phenomena have a different synchronization mechanism from the case of white noise.