On a coupled relaxation oscillation
Abstract
An analytic investigation is presented for a piecewiselinear version of a twocoupled relaxation oscillator. The circuit dynamics are described by a fourdimensional piecewiselinear differential equation containing two small parameters (epsilon 1, epsilon 2). In the case of (epsilon 1, epsilon 2)  0, the phase space of the system degenerates into four overlapping halfplanes connected by a transitional condition. Then the Poincarereturn map is derived rigorously as a onedimensional homeomorphism of the circle. The mapping is shown to account for the fact that the actual circuit exhibits various complicated synchronous phenomena and asynchronous phenomena.
 Publication:

IEEE Transactions on Circuits Systems
 Pub Date:
 September 1988
 Bibcode:
 1988ITCS...35.1147S
 Keywords:

 Coupled Modes;
 Poincare Problem;
 Relaxation Oscillators;
 Differential Equations;
 Linear Equations;
 Waveforms;
 Electronics and Electrical Engineering