Analyze the stability of the critical point of the following system, proposing as a Lyapunov function V(x,y)=ax2m+by2n. a) x′=−2xy, y′=x2−y3
Analyze the stability of the critical point of the following system, proposing as a Lyapunov function V(x,y)=ax2m+by2n. a) x′=−2xy, y′=x2−y3
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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Analyze the stability of the critical point of the following system, proposing as a Lyapunov function V(x,y)=ax2m+by2n.
a) x′=−2xy, y′=x2−y3
b) x′=xy2−(x3/2), y′=−(y3/2)+(yx2/5)
c) Show that x′=−2x+xy3, y′=−x2y2−y3 is asymptotically stable.
Pleas be as clear as possible and legible. Show and explain all the steps in detail. Thank you very much.
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