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- Richard H. Rand
- SIAM Review
- 1996

- Richard H. Rand
- 2003

This manuscript is among the initial offerings being published as part of a new approach to scholarly publishing. The manuscript is freely available from the The online version of this work is available on an open access basis, without fees or restrictions on personal use. A professionally printed and bound version may be purchased through Cornell Business… (More)

- A H Cohen, P J Holmes, R H Rand
- Journal of mathematical biology
- 1982

We present a theoretical model which is used to explain the intersegmental coordination of the neural networks responsible for generating locomotion in the isolated spinal cord of lamprey. A simplified mathematical model of a limit cycle oscillator is presented which consists of only a single dependent variable, the phase theta(t). By coupling N such… (More)

We show that explicit mathematical and biological relationships exist among the scaling exponents and the allometric constants (a and b, respectively) of log–log linear tree-community size frequency distributions, plant density N T , and minimum, maximum and average stem diameters (D min , D max , and D D, respectively). As individuals grow in size and D… (More)

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, +5 authors Harold Craighead
- 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)

- D Dane Quinn, Richard H Rand, Steven H Strogatz
- Physical review. E, Statistical, nonlinear, and…
- 2007

The Winfree model consists of a population of globally coupled phase oscillators with randomly distributed natural frequencies. As the coupling strength and the spread of natural frequencies are varied, the various stable states of the model can undergo bifurcations, nearly all of which have been characterized previously. The one exception is the unlocking… (More)

- Maxim Zalalutdinov, Jeevak Parpia, +4 authors Richard Rand
- 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)