1. Modelling two competing species Consider a two-species ecosystem in which both species compete for the same food supp

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1 Modelling Two Competing Species Consider A Two Species Ecosystem In Which Both Species Compete For The Same Food Supp 1 (82.21 KiB) Viewed 38 times

1. Modelling two competing species Consider a two-species ecosystem in which both species compete for the same food supply. (a) Assuming that each species in isolation obeys a logistic growth law. Derive the following system of coupled ODEs for the popu- lation dynamics. State any additional assumptions clearly. i - mry, (la) ý cy – dy? – Nry. (lb) = ac – = = (b) Assuming that the species are virtually identical: a = c=1 and b=d=1, but n + m, find the fixed points of equations (la,b). (c) Find an explicit expression for the gradient of solutions in the phase plane dy/dr, still assuming that a = b = c = d = 1 and that n = 2, m = 3. Find equations for the isoclines along which the gradient is zero and along which it is infinite. (d) Sketch the direction field and typical solution trajectories in the phase plane for the parameters given in part (c). Can the two species co-exist? =