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