## シリコンチップ上に構成する３変数Lotka-Volterra系の空間不安定性解析

## 神谷 泰史

2005 年度 卒 ／修士（工学）

## 修士論文の概要

In nature, we can observe various nonlinear phenomena such as chaos and reaction diffusion systems. These phenomena can be partly modeled. For example, the Lorentz system can be modeled in terms of a nonlinear oscillator. Moreover, a spatiotemporal system can also be modeled in terms of a coupled oscillator system. In this system, the oscillators connect each other.

Technological applications using a nonlinear oscillator system such as chaotic communication and data encryption has been studied. So that apply the nonlinear oscillator system for such applications, a nonlinear oscillator model must be fabricated on integrated circuit. Therefore, a 2-prey 1-predator Lotka-Volterra system that has a simple expression is fabricated, and this system represents various nonlinear oscillations.

In this thesis, I fabricated an analog integrated circuit that implements a 2-prey 1-predator Lotka-Volterra oscillator. Since the integrated circuit has a compact structure, many circuits can be arranged on a silicon chip. Thus, a two-dimensional structure, that is a diffusive Lotka-Volterra system, can be constructed. In this system, I estimated spatial instability conditions that the system represents a spatial behavior such as spatial localized patterns by theoretical analysis. Moreover, I conducted numerical simulations under the spatial instability conditions, and spatial localized patterns were obtained in the diffusive Lotka-Volterra system.