Lotka-Volterra Model. The following Lotka-Volterra equations are a Kolmogorovtype model of predator-prey relationships for interacting populations, e.g. hosts and parasites, yeasts and sugars, sharks and surfers. xΛ1β=p1βx1ββp2βx1βx2βxΛ2β=p3βx2β+p1βp4βx1βx2ββx1β(0)=x10βx2β(0)=x20ββ Parameters p1β to p4β are constant death and birth rates; x1β is the host population, x2β is the parasite population, and the product x1βx2β represents the "getting-together" of the two species. a) Find the equilibrium steady state solutions for these equations, [xeβyeβ]T=xeβ in terms of the parameters.
