Bifurcation phenomena may be examined in terms of the class of non-linear differential equations of the first kind in the form x(t) = alpha(n) beta x(t) - {x(t)}(n+1), where alpha and beta are constants and n is an integer. A transformation of variables is applied taking into account the initial values x(0) = x(0). The solutions are presented in the form of dimensionless variables and in polar coordinates to visualize limit cycles. The well known logistic and pitchfork equations (n = 1 and 2, respectively) are special cases, as is also the equation for explosive population growth (n = 1, alpha and beta imaginary).