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Find the steady states of these two equations:

My working out as far:

\[ 0=u*(1-u*)(a+u*)-u*v* \]

\[ 0=v*(bu*-c) \]

I looked at the 2nd equation first giving:

\[ v*=0, u*=c/b \]

subbing v*=0 into equation 1 gave:

\[ 0=u*(1-u*)(a+u*) \]

\[ u*=0, u*=1, u*=-a \]

\[ v=a+c/b - ac/b-c^2/b^2 \]

Not sure about that part of the steady state question so any help would be really helpful, cheers

Giving three steady states of

(0,0), (1,0), (-a,0)

Then I looked at subbing u*=b/c. (However this part of my working got confusing and I'm not entirely sure if it was correct.

\[ 0=c/b(1-c/b)(a+c/b)-cv/b \]

\[ cv/b=c/b-c^2/b^2(a+c/b) \]