Show that the system x = y - x, y = -4x- y. is not a...
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Show that the system x = y - x³, y = -4x- y³. is not a gradient system, but has a Lyapunov function of the form (3) - Ax² + By², for some constants A, B € R. Find A, B and sketch the phase portrait near the origin. V: R³ → R; Show that the system x = y - x³, y = -4x- y³. is not a gradient system, but has a Lyapunov function of the form (3) - Ax² + By², for some constants A, B € R. Find A, B and sketch the phase portrait near the origin. V: R³ → R;
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To show that the given system is not a gradient system we need to demonstrate that there is no potential function whose gradient matches the vector field of the system Lets assume there exists a poten... View the full answer
Related Book For
Numerical Methods With Chemical Engineering Applications
ISBN: 9781107135116
1st Edition
Authors: Kevin D. Dorfman, Prodromos Daoutidis
Posted Date:
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