Determine the stability of the equilibrium points


Stability and Lyapunov functions

Solve the following problem

Consider the system x' = f(x), where f: R^2 into R^2, is defined by:

f(x) = [ (x1)^3 + (x1) (x2)^2 ]

[ (x1)^2 (x2) + (x2)^3 ]

a- Find all equilibrium points of the system.

b- Use an appropriate Lyapunov function to determine the stability of the equilibrium points. If an equilibrium point is stable, is it asymptotically stable ?

 

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Engineering Mathematics: Determine the stability of the equilibrium points
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