Delay-induced stabilization of coupled oscillators

Abstract

Delays can have a negative impact on the stability of various systems. However, it was reported that the transmission delays of signals among oscillators can stabilize unstable equilibrium points in coupled oscillators, which is called amplitude death (AD). AD caused by delays has been extensively researched in the field of nonlinear science and has attracted attention for various engineering applications. In this article, we review the latest studies on AD caused by delays in oscillator networks, in particular those that considered heterogeneous delays and time-varying networks.

Amplitude Death in Coupled Oscillators: An Approach from Robust Stability

“…複数の発振器が相互に影響を与える「結合発振器」には，興 味深い様々な現象が生じる (1)， (2) ．その中でも，複数の発振器に 拡散的な結合を施すことで，それらの発振が「止まる」現象は， 1980 年代から注目を集め (3) - (6) ，その学術的な魅力は現在も色あ せていない (7) - (11) ．この現象は， 「Oscillation Death」と「Amplitude Death」 (注1) (12) に分類される (8) E-mail konishi-ees@omu.ac.jp 杉谷栄規 正員 茨城大学工学部 E-mail yoshiki.sugitani.0301@vc.ibaraki.ac.jp Keiji KONISHI, Member (Graduate School of Engineering, Osaka Metropolitan University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan), and Yoshiki SUGITANI, Member (College of Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511 Japan).…”

Adaptive Memoryless Sliding Mode Control of Uncertain Rössler Systems with Unknown Time Delays

“…In this paper [25], an robust adaptive controller has been developed to asymptotically stabilize a class of uncertain nonlinear systems with the assumed unknown and bounded disturbances. In recent years, many researchers have found that systems are often affected by time delays, resulting in complex behaviors of the systems, such as loss of stability, bifurcation, and chaos [2,[25][26][27][28][29][30][31][32][33]. Among them, the one-dimensional dynamical system with delay will produce high-dimensional chaotic phenomena, which will affect the state responses of the systems [34,35].…”