5. Give an example of a nonlinear system that has an equilibrium point for which the linearized…

5.           Give an example of a nonlinear system that has an equilibrium point for which the linearized system has a zero eigenvalue, but the nonlinear system has only one equilibrium point.

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6.           For the system

 

x' = y – 1

y' = y x2,

 

determine the types of each equilibrium point.

7.          For the system

 

x' = sin(x)

y' = cos(y),

 

find all equilibrium points and use linearization together with the nullclines to sketch the phase plane.