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- Richard H Rand, R Rand, Nonlinear Vibrations
- 2005

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)

- Karl J Niklas, Jeremy J Midgley, Richard H Rand, South Town, Africa
- 2003

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)

- N R Adiga, G Almasi, G S Almasi, Y Aridor, R Barik, D Beece +195 others
- 2002

LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be… (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)

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)

- Geoffrey Recktenwald, Richard Rand
- 2005

Coexistence phenomenon refers to the absence of expected tongues of instability in parametrically excited systems. In this paper we obtain sufficient conditions for coexistence to occur in the generalized Ince equation (1 + a 1 cos t + a 2 cos 2t) ¨ v + (b 1 sin t + b 2 sin 2t) ˙ v + (+ c 1 cos t + c 2 cos 2t)v = 0. The results are applied to the stability… (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)