Stability Analysis of the Logistic Model

The mortality rate is greater than the birth rate. One of the two stationary solutions has a physical meaning Xo = 0. The other solution would correspond to a negative population and thus has no physical meaning. The Xq = 0 solution is stable and would return to extinction under the effect of a perturbation  

The birth rate is greater than the mortality rate. The two solutions have a physical meaning. The Xo = 0 branch becomes unstable while the stable branch corresponds to Xo = K. One observes a bifurcation at point Xo = 0  

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