Lotka-Volterra Competitive Population Model

Solves the Lotka-Volterra Competitive(logistic) model for two species using the ode45 solver.

Solves the Lotka-Volterra Competitive(logistic) model for two species.

Species 1: dx1/dt = alpha1*x1[(K1-x1-beta*x2)/K1]
Species 2: dx2/dt = alpha2*x2[(K2-x2-gamma*x1)/K2]

where; K1&2 = carrying capacity, alpha1&2 = growth rate, beta & gamma = inter-dependence of species.
Four cases are simulated based on the initial conditions (initial population of the species) and constant parameters (growth rates and species inter-dependence).