Dynamics of microbubble oscillators with delay coupling

作者：Heckman C R; Sah S M; Rand R H^*

来源：Communications in Nonlinear Science & Numerical Simulation, 2010, 15(10): 2735-2743.

DOI：10.1016/j.cnsns.2009.10.017

• Microbubble
• Differential delay equation
• Perturbation theory
• Hopf bifurcation

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.

• 出版日期2010-10