グラフ上の反応拡散方程式と自律分散システム

• 湯浅 秀男

  東京大学大学院工学系研究科 名古屋大学大学院工学研究科 理化学研究所バイオ・ミメティックコントロール研究センター

• 伊藤 正美

  理化学研究所バイオ・ミメティックコントロール研究センター

書誌事項

タイトル別名

• Autonomous Decentralized Systems and Reaction-Diffusion Equation on a Graph
• グラフ ジョウ ノ ハンノウ カクサン ホウテイシキ ト ジリツ ブンサン システム

抄録

Some kinds of spatiotemporal pattern generator systems are expressed by evolution equations. Such evolution equations are composed of many dynamic units which behave from only its local information. This is one example to coordinate many subsystems which observe the system from inside and to generate a global order. This paper shows how to treat these evolution equations and how to apply it to network systems. First, a continuous media system which is expressed by a gradient system in function space is considered. One of the simplest potential functional derives a reaction diffusion equation which decreases the value of potential functional monotonously. The similar result is found in graph space. That is, a reaction diffusion equation on a graph decreases the value of a potential functional monotonously. This means that a network of dynamic units which observe only their connecting units' states can generate a global order in the same way of continuous media. This theory can treat some internal dynamic network system which should coordinate without some kinds of central controllers.

収録刊行物

• 計測自動制御学会論文集

  計測自動制御学会論文集 35 (11), 1447-1453, 1999

  公益社団法人 計測自動制御学会

キーワード

• graph
• gradient system
• potential functional
• reaction-diffusion equation
• autonomous decentralized system

詳細情報

• CRID: 1390282679478674944
• NII論文ID: 130003970822
• NII論文ID: 10004577393
• NII書誌ID: AN00072392
• DOI: 10.9746/sicetr1965.35.1447
• ISSN: 18838189
• ISSN: 04534654
• NDL書誌ID: 4925077
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I4925077
• Web Site: https://www.jstage.jst.go.jp/article/sicetr1965/35/11/35_11_1447/_pdf
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