Editing Competitive Lotka–Volterra equations (section)

===''N'' species===
This model can be generalized to any number of species competing against each other.  One can think of the populations and growth rates as [[vector (geometric)|vectors]], {{mvar|α}}'s as a [[matrix (mathematics)|matrix]].  Then the equation for any species {{mvar|i}} becomes
<math display="block">\frac{dx_i}{dt} = r_i x_i \left(1- \frac{\sum_{j=1}^N \alpha_{ij}x_j}{K_i} \right) </math>
or, if the carrying capacity is pulled into the interaction matrix (this doesn't actually change the equations, only how the interaction matrix is defined),
<math display="block">\frac{dx_i}{dt} = r_i x_i \left( 1 - \sum_{j=1}^N \alpha_{ij}x_j \right) </math>
where {{mvar|N}} is the total number of interacting species.  For simplicity all self-interacting terms {{math|''α''<sub>ii</sub>}} are often set to 1.