MORSE THEORY AND LIAPUNOV FUNCTIONS,
Abstract
When an autonomous system of differential equations dx/dt = f(x) (x = x sub i, x sub 2, . . . , x sub n has an isolated equilibrium point at (x) = (0) which is asymptotically stable, it is of interest to determine a region of attraction containing the equilibrium point; that is, a region R with the property that every half-trajectory which has a point in R when t = t sub 0 tends to the equilibrium point at the origin as t approaches infinity. It is shown how methods due to Morse can be used with great effectiveness in the determination of such regions of attraction. A new condition for global asymptotic stability of the equilibrium point then emerges in a natural fashion.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1964
- Accession Number
- AD0622528
Entities
People
- Walter Leighton
Organizations
- Case Western Reserve University