Consider the autonomous system: dx/dy= x^3-y^3 dy/dt = 2xy^2+4x^2y+2y^2. Construct a Lyapunov function of the form V (x, y) = ax2 + cy2
, where a and c are to be determined, to show that
the single critical point of the system at the origin is unstable.
Transcribed Image Text:dx = x³ — y³, dy = 2xy² + 4x²y + 2y³. dt dt Construct a Lyapunov function of the form V(x, y) = ax²+ cy², where a and c are to be determined, to show that the single critical point of the system at the origin is unstable.

Question

Consider the autonomous system: dx/dy= x^3-y^3 dy/dt = 2xy^2+4x^2y+2y^2. Construct a Lyapunov function of the form V (x, y) = ax2 + cy2
, where a and c are to be determined, to show that
the single critical point of the system at the origin is unstable.

dx
= x³ — y³,
dy
=
2xy² + 4x²y + 2y³.
dt
dt
Construct a Lyapunov function of the form V(x, y) = ax²+ cy², where a and c are to be determined, to show that
the single critical point of the system at the origin is unstable.

Accepted Answer

Step 1:  Step 2: Explanation:Here it already says in question that system is unstable at origin so…