ON CERTAIN RELAXATION OSCILLATIONS: CONFINING REGIONS,
Abstract
Relaxation oscillations described by the generalized Lienard equation are investigated in the phase and Lienard planes. When f(x), g(x), and F(x) = integral evaluated from 0 to x f(u)du are subject to certain restrictions, a number of analytic curves can be obtained in these planes which serve as bounds on solution trajectories. Piece-wise connection of such bounding curves provide explicit annular regions with the property that solution trajectories on the boundary of an annulus move to the interior with increasing time, t. The Poincare-Bendixson theorem then guarantees at least one periodic orbit within such an annulus. It is shown that the periodic orbits which are isolated by this means are unique within the annulus, hence orbitally stable.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1964
- Accession Number
- AD0603688
Entities
People
- Nelson Wax
- Peter James Ponzo
Organizations
- University of Illinois Urbana–Champaign