title: Stabilization of a steady state in network oscillators by using diffusive connections with two long time delays.
abstract: The present study shows that diffusive connections with two long-time delays can induce the stabilization of a steady state in network oscillators. A linear stability analysis shows that, if the two delay times retain a proportional relation with a certain bias, the stabilization can be achieved independent of the delay times. Furthermore, a simple systematic procedure for designing the coupling strength and the delay times in the connections is proposed. The procedure has the following two advantages: one can employ time delays as long as one wants and the stabilization can be achieved independently of its network topology. Our analytical results are applied to the well-known double-scroll circuit model on a small-world network.
authors.affiliation: Department of Electrical and Information Systems, Osaka Prefecture University, Sakai, Osaka, Japan.
authors.forename: Keiji
authors.initials: K
authors.lastname: Konishi
authors.forename: Hideki
authors.initials: H
authors.lastname: Kokame
authors.forename: Naoyuki
authors.initials: N
authors.lastname: Hara