Design of robust network dynamics against noises and its thermodynamical characterization

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540417
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Osaka Electro-Communication University
• Principal Investigator: YANAGITA Tatsuo 大阪電気通信大学, 工学部, 教授 (80242262)
• Co-Investigator(Kenkyū-buntansha): NAKAO Hiroya 東京工業大学, 情報理工学(系)研究科, 准教授 (40344048)
• Research Collaborator: MIKHAILOV Alexander Friz Haber Institure of the Max Plank Society
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ネットワーク / 同期 / 熱力学的特性 / マルコフ連鎖モンテカルロ法 / 振動子 / 比熱異常 / Shottky anomaly

Outline of Final Research Achievements

There are many functional systems with robust against noises in nature, e.g., chemical reactions in cells and neural networks. We have designed network dynamics having given function with robust against noises through the Markov chain Monte Carlo method. We have considered networks of phase oscillators and designed its connection networks to show better synchronization performance against noises. To do this, we have used the inverse of the sum of eigenvalues of the Laplacian matrix for network as a "synchronization performance" for the Markov chain method. Our designed networks showed a structural transition from core-periphery to interlaced network with increasing number of nodes. The method enabled us to characterize network thermodynamically. For smaller number of nodes, we found that the heat capacity had a peak called the Shottky anomaly in statistical mechanics, which comes from energy (corresponding to the synchronization performance) gap between highly optimization networks.

Free Research Field

非線形数理科学