On Lotka-Volterra model of interacting species

Abstract:

In this lecture we have discussed the dynamical behaviours of the basic mathematical model of two interacting prey and predator species devised by Lotka and independently by Volterra around 1925. This is the starting model of Mathematical Ecology. This model has two equilibrium (or steady state) positions, one is trivial equilibrium position and another is non-trivial equilibrium position. The trivial equilibrium position is always unstable and the non-trivial equilibrium position is stable but not asymptotically, this is so because this model has no internal mechanism to stabilize (asymptotically) the non-trivial equilibrium position. Next we have discussed the effects of intraspecific competition among the prey population of this model. Here we have also discussed several possible modifications of this model.