\item Compute all the equilibria of this system, study their stability, and characterize those that are hyperbolic (attractive or repulsive node or focus, or saddle point);
\item Compute all the equilibria of this system, study their stability, and characterize those that are hyperbolic (attractive or repulsive node or focus, or saddle point);
\item Write the linearized system around the origin. Ex^press all its trajectories as a function of time and initial state;
\item Write the linearized system around the origin. Express all its trajectories as a function of time and initial state;
\item For each asymptotically stable equilibrium, give a compact set the interior of which is not empty that is included in the basin of attraction. Assuming that an orbit starts in that set, can you give an upper bound on the time it needs to enter the closed disk centered at the equilibrium and of radius \(\epsilon\) ? Your answer can be valid only for sufficiently small \(\epsilon\) ;
\item For each asymptotically stable equilibrium, give a compact set the interior of which is not empty that is included in the basin of attraction. Assuming that an orbit starts in that set, can you give an upper bound on the time it needs to enter the closed disk centered at the equilibrium and of radius \(\epsilon\) ? Your answer can be valid only for sufficiently small \(\epsilon\) ;
\item Draw the equilibria and the set given at the preceding subquestion in the state plane.
\item Draw the equilibria and the set given at the preceding subquestion in the state plane.
