6. Construct a suitable Lyapunov function of the form ax? + cy?, where a and c are to be determined, then show that the critical point at the origin is asymptotically stable, for the system: a' = -a³...

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Extracted text: 6. Construct a suitable Lyapunov function of the form ax? + cy?, where a and c are to be determined, then show that the critical point at the origin is asymptotically stable, for the system: a' = -a³ + xy", 3/ = -2a²y – y*. 7. Analyse the following system y – 3r(x² + y³), y' = x + 3y – 3y(x² + y?). and show that is has an equilibrium point at the origin and one periodic orbit.