If we have this nonlinear system
$$ x ̇ = −x + 0.1y + x^2 y $$
$$ y ̇ = b − 0.1y − x^2y $$ What kind of bifurcations happen as you vary b ∈ [0,1]?
I managed to solve for equilibriums at the source and $$ x = b \space \& \space y = \frac{b}{(0.1 + b^2)} $$
aaand that's where I get a little lost. I tried making a Jacobian matrix and using that to linearize at the equilibrium points (can maybe do some trace determinant analysis) but I don't think I was able to put it together.
Any help or guidance would be appreciated.