Question

Question 1: (5 marks) Consider a two-species model for populations Ni and N2 follows as N1 (a -bN1 cN2) dt N2 (d - eN2 - Ni) dt (a) What kind of interaction does this system of equations represent? (b) Show that the equations can be simplified to dn1 an n1 (1 d7 dn2 Bn2 (1n2-n1). dT mT into the system of equations and picking by substituting N = kn\, N2 = ln2 and t appropriate constants k, l and m dt (a) What kind of interaction does this system of equations represent? (b) Show that the equations can be simplified to dn1 n1 (1 1-an2) d7 dn2 Bn2 (1--n) dT by substituting N, kn1, N2 ln2 and t mT into the system of equations and picking appropriate constants k, l and m (c) Find the equilibrium populations for this system. When will there be three equilibria and when will there be four equilibria? (d) Let a 3, B = 4 and y 2, and classify each equilibrium point as either stable or unstable. Can both species co-exist? (That is, is there a stable solution with both populations non-zero?)

Answer 1

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