A species interaction model (Q1102230)

One model describing the behavior of interacting components is based upon the Lotka-Volterra equations for interacting species: \[ dN_ i/dt=\alpha_ iN_ i+\sum^{n}_{j=1}\beta_{ij}N_ iN_ j,\quad i=1,2,3,...,n, \] where \(N_ i\) is the population of species i, n is the number of interacting species and \(\alpha_ i\) and \(\beta_{ij}\) are constants. The Lotka-Volterra equations will be used to model a predator- prey system with \(n=2\). We will also discuss how the model can be utilized in determining harvesting policy.