卒業生とその進路

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.

学術論文

  1. Asai T., Kamiya T., Hirose T., and Amemiya Y., "A subthreshold analog MOS circuit for Lotka-Volterra chaotic oscillator," International Journal of Bifurcation and Chaos, vol. 16, no. 1, pp. 207-212 (2006).

国際会議

  1. Ota K., Yamaguchi M., Berdan R., Marukame T., Nishi Y., Matsuo K., Takahashi K., Kamiya T., Miyano S., Deguchi J., Fujii S., and Saitoh M., "Performance Maximization of In-Memory Reinforcement Learning with Variability-Controlled Hf1-xZrxO2 Ferroelectric Tunnel Junctions," 2019 IEEE International Electron Devices Meeting (IEDM), Hilton San Francisco Union Square hotel, San Francisco, USA (Dec. 7-11, 2019).
  2. Kamiya T., Motoike I.N., and Asai T., "Spatial pattern formation of diffusive Lotka-Volterra system on analog integrated circuits," Proceedings of the XXV Dynamics Days Europe, pp. 60-61, Berlin, Germany (Jul. 25-28, 2005).

国内学会

  1. 神谷 泰史, 浅井 哲也, "二次元拡散・三変数Lotka-Volterra系における空間パターンの発生," 数理モデル化と問題解決シンポジウム論文集, pp. 225-232, (名古屋), 2006年10月.
  2. 神谷 泰史, 元池 N. 育子, 浅井 哲也, "アナログLSI上に実装した拡散Lotka-Volterra系における空間パターンの発生," 日本物理学会秋季大会, (京都), 2005年9月.
  3. 神谷 泰史, 金澤 雄亮, 浅井 哲也, 雨宮 好仁, "サブスレッショルド領域で動作するアナログCMOS回路によるカオス発生器," 電子情報通信学会総合大会, (仙台), 2003年3月.