Relaxation Oscillators with Exact Limit Cycles
نویسندگان
چکیده
منابع مشابه
Variational approach to a class of nonlinear oscillators with several limit cycles.
We study limit cycles of nonlinear oscillators described by the equation x + nuF(x) + x = 0 with F an odd function. Depending on the nonlinearity, this equation may exhibit one or more limit cycles. We show that limit cycles correspond to relative extrema of a certain functional. Analytical results in the limits nu-->0 and nu-->infinity are in agreement with previously known criteria. For inter...
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Thetiming jitter in relaxation oscillators is analyzed. This jitter is described by a single normalized equation whose solution allows prediction of noise in practical oscillators. The theory is confirmed by measurements on practical oscillators and is used to develop a prototype low noise oscillator with a measured jitter of 1.5 ppm rms.
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We study networks of relaxation oscillators coupled with time delay synapses. A pair of oscillators is analyzed and shown to attain loosely synchronous solutions for a wide range of initial conditions and time delays. Simulations of one and two dimensional oscillator networks indicate that locally coupled oscillators are also loosely synchronous. Desynchronous solutions are possible when system...
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Relaxation oscillators can usually be represented as a feedback system with hysteresis. The relay relaxation oscillator consists of relay hysteresis and a linear system in feedback. The objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators. In particular, we give a complete analysis for the case of unimodal periodic orbits, and illustr...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1998
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5746