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Verify that the following function is a Lyapunov function for both systems and check if it is a strict Lypaunov function: L(x, y) = 1/4(1 − x^2)^2 +1/4y^4

Verify that the following function is a Lyapunov function for both systems and check if it is a strict Lypaunov function: L(x, y) = 1/4(1 − x^2)^2 +1/4y^4

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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Verify that the following function is a Lyapunov function for
both systems and check if it is a strict Lypaunov function:
L(x, y) = 1/4(1 − x^2)^2 +1/4y^4
Based on this Lyapunov function, classify the equilibria you found in the
previous part as ‘Asymptotically Stable’, ‘Stable’, or ‘Inconclusive’.

a'(t) = x · (1 – a²), y/(t) = -y³
Transcribed Image Text:a'(t) = x · (1 – a²), y/(t) = -y³
a'(t) = y", y(t) = x · (1 – a²)
Transcribed Image Text:a'(t) = y", y(t) = x · (1 – a²)
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