Regular Article

Amplitude death in oscillators coupled by asymmetric connection delays with tree graph topology

¹ Department of Electrical and Electronic Engineering, Ibaraki University 4-12-1 Nakanarusawa, Hitachi, Ibarak 316-8511, Japan
² Department of Electrical and Information Systems, Osaka Prefecture University 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan

^a e-mail: yoshiki.sugitani.0301@vc.ibaraki.ac.jp

Received: 8 January 2020
Received in final form: 23 April 2020
Published online: 6 July 2020

Abstract

The present study investigates amplitude death in an oscillator network with asymmetric connection delays and a tree graph topology. A frequency domain analysis reveals that the local steady-state stability is dominated by the sum of the connection delays between connected oscillators. Based on this observation, we show that the local steady-state stability can be reduced to that with symmetric connection delays, as long as the sum of the connection delays between connected oscillators satisfies a certain condition. Numerical simulations verify the analytical results.