Networks of passive oscillators

Author

Kulkarni, Vishwesh V. ; Riedel, Marc ; Stan, Guy-Bart

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Minnesota, Minneapolis, MN, USA

fYear

2011

fDate

28-30 Sept. 2011

Firstpage

559

Lastpage

565

Abstract

We present new results on the synthesis of globally stable limit cycles in networks of passive oscillators. These passive oscillators can be represented as a modified multi- input-multi-output (MIMO) Lure´ system that is dissipative with respect to a certain supply rate. We use KS multipliers to establish the conditions under which the system undergoes either Hopf bifurcation or a pitchfork bifurcation. Under these conditions the network exhibits oscillations. Our results are applicable to networks of non-identical oscillators so long as the each oscillator is a passive oscillator.

Keywords

bifurcation; biomedical electronics; oscillators; Hopf bifurcation; KS multipliers; MIMO Lure system; multiple-input multiple-output Lure system; passive oscillators; pitchfork bifurcation; Asymptotic stability; Bifurcation; Limit-cycles; MIMO; Manifolds; Oscillators; Stability analysis; Hopf bifurcation; KS multipliers; Lure´ systems; Zames-Falb multipliers; global stability; oscillators; pitchfork bifurcation;

fLanguage

English

Publisher

ieee

Conference_Titel

Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on

Conference_Location

Monticello, IL

Print_ISBN

978-1-4577-1817-5

Type

conf

DOI

10.1109/Allerton.2011.6120216

Filename

6120216