Geoffrey Recktenwald6
Lauren Lazarus4
6Geoffrey Recktenwald
4Lauren Lazarus
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In this work we study a system of two van der Pol oscillators, x and y, coupled via a ''bath'' z: € x À ð1 À x 2 Þ_ x þ x ¼ kðz À xÞ € y À ð1 À y 2 Þ_ y þ y ¼ kðz À yÞ _ z ¼ kðx À zÞ þ kðy À zÞ We investigate the existence and stability of the in-phase and out-of-phase modes for parameters > 0 and k > 0. To this end we use Floquet theory and numerical(More)
  • Keith Aubin, Maxim Zalalutdinov, Tuncay Alan, Robert Reichenbach, Richard Rand, Alan Zehnder +2 others
  • 2004
— Limit cycle, or self oscillations can occur in a variety of NEMS devices illuminated within an interference field. As the device moves within the field, the quantity of light absorbed and hence the resulting thermal stresses changes, resulting in a feedback loop that can lead to limit cycle oscillations. Examples of devices that exhibit such behavior are(More)
  • Maxim Zalalutdinov, Jeevak Parpia, Keith Aubin, Harold Craighead, Tuncay Alan, Alan Zehnder +1 other
  • 2003
Self-sustained mechanical vibrations of a disc-type micro-fabricated resonator were experimentally observed when a continuous wave (CW) laser beam was focused on the periphery of the disc (for a 40 µm diameter resonator, natural frequency 0.89MHz, the laser power above a 250 W threshold was required). A theoretical model for self-oscillatory behavior has(More)
We study a system of three limit cycle oscillators which exhibits two stable steady states. The system is modeled by both phase-only oscillators and by van der Pol oscillators. We obtain and compare the existence, stability and bifurcation of the steady states in these two models. This work is motivated by application to the design of a machine which can(More)
In this work, a differential delay equation (DDE) with a cubic nonlinearity is analyzed as two parameters are varied by means of a center manifold reduction. This reduction is applied directly to the case where the system undergoes a Hopf-Hopf bifurcation. This procedure replaces the original DDE with four first-order ODEs, an approximation valid in the(More)
We investigate the dynamics of a system of two van der Pol oscillators with delayed velocity coupling. We use the method of averaging to reduce the problem to the study of a slow-flow in three dimensions. We study the steady state solutions of this slow-flow, with special attention given to the bifurcations accompanying their change in number and stability.(More)