Editing Lotka–Volterra equations (section)

===Population equilibrium===
Population equilibrium occurs in the model when neither of the population levels is changing, i.e. when both of the derivatives are equal to 0:
<math display="block">x(\alpha - \beta y) = 0,</math>
<math display="block">-y(\gamma - \delta x) = 0.</math>

The above system of equations yields two solutions:
<math display="block">\{y = 0,\ \  x = 0\}</math>
and
<math display="block">\left\{y = \frac{\alpha}{\beta},\ \  x = \frac{\gamma}{\delta} \right\}.</math>

Hence, there are two equilibria.

The first solution effectively represents the extinction of both species. If both populations are at 0, then they will continue to be so indefinitely. The second solution represents a fixed point at which both populations sustain their current, non-zero numbers, and, in the simplified model, do so indefinitely. The levels of population at which this equilibrium is achieved depend on the chosen values of the parameters ''α'', ''β'', ''γ'', and ''δ''.