
1 For each of the following systems 
a) show 
 EMBED Equation  
		is a Lyapunov function for the system.
b) show  EMBED Equation  is an equilibrium point of the system.
c) show  EMBED Equation  is a stationary point for  EMBED Equation  
d) determine the type of stationary point  by looking at the eigenvalues of the Hessian matrix
e) determine the stability of the equilibrium point.

  	A)    EMBED Equation  	 EMBED Equation  
	  B)    EMBED Equation  	 EMBED Equation  
  C)    EMBED Equation  	 EMBED Equation  	
     
2 Repeat question (1) for
 EMBED Equation  
and the following systems
	a)    EMBED Equation  	 EMBED Equation  
b)    EMBED Equation  	 EMBED Equation  

3 Show that the system
 EMBED Equation  
has no closed orbits by construsting a Lyapunov function 
 EMBED Equation  
with suitable a and b.

