Taiji Yamada

Chaotic neural networks and the traveling salesman problem

Deterministic chaos is not only a profound scientific concept but also ubiquitously found in both natural and artificial real-world systems. From the viewpoint of engineering, the deterministic chaos has many possible applicabilities. In this report, the authors study the application of chaotic neural networks (CNN) to the traveling salesman problem (TSP) as a concrete example of possible application of deterministic chaos. First, a neuron model with chaotic dynamics, which comprises CNN as the element, is explained and its nonlinear dynamics are demonstrated. Second, the network representations for neurocomputing approaches to TSPs are described. Last, it is shown that CNN have high ability to solve TSPs.

Nonlinear Neurodynamics and Combinatorial Optimization in Chaotic Neural Networks

In this article we study the spatiotemporal complex dynamics of chaotic neural networks and their relationships with combinatorial optimization. In particular, we apply chaotic neural networks to the traveling salesman problem as a typical example of combinatorial optimization problems and analyze the nonlinear computational dynamics by comparing its characteristics with those of other dynamical models.

Nonlinear analyses of roll motion of a flooded ship in waves

This paper investigates nonlinear responses of a flooded ship in regular waves. In previous experimental work, we found that the roll motion of a flooded ship can exhibit complicated irregular behaviour even in waves of a moderate height. First, we analyse the fractal dimension and the Lyapunov exponents of the experimental data and show that they have chaotic characteristics. We also show that a radial basis function network obtained directly from the data can reproduce a geometrical structure of the reconstructed attractor and provide good short-term prediction on the dynamical motion. Next, in order to understand this nonlinear phenomenon, we derive a simple mathematical model for the nonlinearly coupled motion of roll and flooded water in regular waves. This model has a form of coupled Duffings equations with a bistable restoring term and a nonlinear inertial coefficient matrix. We obtain bifurcation diagrams of periodic solutions of this model and examine the intricate structure of this nonlinear system. Chaotic responses are found in wide regions of the parameter space, even if the wave-exciting moment is not large. Furthermore, the attractor structure of the chaotic solution is similar to that of the measured chaotic motion in the experiments. The results suggest that bifurcation analyses in this work help us understand the complex dynamics of nonlinear motion of a flooded ship in waves.