Solution Found!
Solved: In each of 1 through 3, construct a suitable Liapunov function of the form ax2 +
Chapter 9, Problem 1(choose chapter or problem)
In each of 1 through 3, construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined. Then show that the critical point at the origin is of the indicated type. dx dt = x3+xy2, dy dt = 2x2 yy3; asymptotically stable
Questions & Answers
QUESTION:
In each of 1 through 3, construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined. Then show that the critical point at the origin is of the indicated type. dx dt = x3+xy2, dy dt = 2x2 yy3; asymptotically stable
ANSWER:Step 1 of 3
We have .
We note that .
We want to check that is an isolated critical point Suppose and . Then we must have and so . Then we must have which is impossible. Hence is the only critical point.