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Dynamics of microbubble oscillators with delay coupling

✍ Scribed by C.R. Heckman; S.M. Sah; R.H. Rand

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
626 KB
Volume
15
Category
Article
ISSN
1007-5704

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✦ Synopsis

We investigate the stability of the in-phase mode in a system of two delay-coupled bubble oscillators. The bubble oscillator model is based on a 1956 paper by Keller and Kolodner. Delay coupling is due to the time it takes for a signal to travel from one bubble to another through the liquid medium that surrounds them. Using techniques from the theory of differential-delay equations as well as perturbation theory, we show that the equilibrium of the in-phase mode can be made unstable if the delay is long enough and if the coupling strength is large enough, resulting in a Hopf bifurcation. We then employ Lindstedt's method to compute the amplitude of the limit cycle as a function of the time delay. This work is motivated by medical applications involving noninvasive localized drug delivery via microbubbles.

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