4. a. Sketch the curve in the trace-determinant plane that the following family of linear systems…

4.           a.    Sketch the curve in the trace-determinant plane that    the following family of linear systems moves along as a changes.

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a    a 1

Y ' = 1           Y

  1    0 )

 

b.          Find all a-values where this system undergoes a bifurcation (i.e.,  the type of the equilibrium point at the origin changes).

 

 

 

5.           Repeat problems 4a and 4b for the system

 

a     2 1

Y ' = 1            Y .

 -2   0 )