We find the steady states by solving the equation 0 = d y d t = 1 2 y ( 1 − y ) . {\displaystyle 0={\frac {dy}{dt}}={\frac {1}{2}}y(1-y).}
Thus, y = 0 {\displaystyle \color {blue}y=0} and y = 1 {\displaystyle \color {blue}y=1} are the steady states.
