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For each of the following systems, find appropriate values of m, n,a, such that V(x, y) = x+ay" is a Liapunov function and hence show that the equilibrium point at the origin is asymptotically stable. x = y − x(x² + y²) d dt d dt y = − x − x²y.

For each of the following systems, find appropriate values of m, n,a, such that V(x, y) = x+ay" is a Liapunov function and hence show that the equilibrium point at the origin is asymptotically stable. x = y − x(x² + y²) d dt d dt y = − x − x²y.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For each of the following systems, find appropriate values of m, n,a, such that V(x, y) = x+ay" is a Liapunov function and hence show that the equilibrium point at the origin is asymptotically stable. x = y − x(x² + y²) d dt d dt y = − x − x²y.
Transcribed Image Text:For each of the following systems, find appropriate values of m, n,a, such that V(x, y) = x+ay" is a Liapunov function and hence show that the equilibrium point at the origin is asymptotically stable. x = y − x(x² + y²) d dt d dt y = − x − x²y.
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