B.3 Consider the Lotka-Volterra model described by dx X – = (x – D) (1+ Y A С dt dy dt -D(0+1 = (y + )(1-- A(1 6). х y С

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B.3 Consider the Lotka-Volterra model described by dx X – = (x – D) (1+ Y A С dt dy dt -D(0+1 = (y + )(1-- A(1 6). х y С 2 D where x(t), y(t) are the interacting species. (a) Find all of the equilibrium solutions of the problem above. (b) For the equilibria where both species takes non negative values, determine whether they are stable or unstable. Determine whether the non negative critical points are spirals, centers, or nodes.