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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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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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