The "Lotka-Volterra model" refers to two separate models of separate kinds of ecological interactions with no deep relationship between them. One is about competition, and the other is about predator-prey interactions. Their dynamical behavior is totally different. The only connection is that they're both named after the same two scientists. In a wide variety of contexts, you'll have to specify which of the Lotka-Volterra models you're referring to in order to make a clue useful.
I think these two are less often confused than they used to be, but I thought I'd just take a minute to clarify so confusion like this never happens again:
This value appears in the denominator of both the Verhulst-Pearl and competitive Lotka-Volterra equations to study predator-prey relationships, as it explains the necessity of both adequate amounts of predators and prey.
Perhaps the most well-known model of competitive exclusion is this set of doubly-eponymous, first-order differential equations that model predator-prey behavior.
The standard version of this model uses an exponential growth curve, though the competitive version incorporates a sigmoidal curve.