finding equilibrium solns and determining their type.

Hi all,

I have been doing some ODE's and came across this question:

Given,

Locate the equilibrium solutions and determine their type for all values of k, including

any bifurcation values.

so first I find the equilibrium solutions:

and find the solutions:

I find the partial derivative with respect to t:

and check solution type:

, is a sink if (No solution) and a source when

similarly,

, is a sink if and a source when (No solution)

So, it is clear that is a source, and is a sink.

I am not sure if my working is right?, If so how do I go ahead and find the bifurcation value? Thanks